View source for Physics equations/07-Work and Energy/Q:lineIntegral/Testbank

<ref>https://en.wikiversity.org/w/index.php?title=Physics_equations/07-Work_and_Energy/Q:lineIntegral&oldid=1378622</ref>
[[Category:Quizbank/bank/Calculus Physics]]
==a07energy_lineIntegral_1_v1==
<quiz display="simple">
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 9xy\hat x +  9.5y^3\hat y </math>, along the y axis from  y = 5 to y = 14}
- a) 7.33E+04  
- b) 7.84E+04  
- c) 8.39E+04  
+ d) 8.98E+04  
- e) 9.60E+04  
</quiz>
{{cot|copies}}
<pre>
===2===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 9.4xy\hat x +  7.5y^3\hat y </math>, along the y axis from  y = 4 to y = 17}
- a) 1.19E+05  
- b) 1.27E+05  
- c) 1.36E+05  
- d) 1.46E+05  
+ e) 1.56E+05  
===3===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 8.2xy\hat x +  7.4y^3\hat y </math>, along the y axis from  y = 5 to y = 12}
- a) 3.25E+04  
- b) 3.48E+04  
+ c) 3.72E+04  
- d) 3.98E+04  
- e) 4.26E+04  
===4===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 7.4xy\hat x +  9.3y^3\hat y </math>, along the y axis from  y = 6 to y = 16}
+ a) 1.49E+05  
- b) 1.60E+05  
- c) 1.71E+05  
- d) 1.83E+05  
- e) 1.96E+05  
===5===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 5.6xy\hat x +  7.9y^3\hat y </math>, along the y axis from  y = 5 to y = 15}
+ a) 9.88E+04  
- b) 1.06E+05  
- c) 1.13E+05  
- d) 1.21E+05  
- e) 1.29E+05  
===6===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 7.9xy\hat x +  8.1y^3\hat y </math>, along the y axis from  y = 5 to y = 12}
- a) 3.32E+04  
- b) 3.56E+04  
- c) 3.81E+04  
+ d) 4.07E+04  
- e) 4.36E+04  
===7===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 8.9xy\hat x +  6.5y^3\hat y </math>, along the y axis from  y = 5 to y = 13}
+ a) 4.54E+04  
- b) 4.86E+04  
- c) 5.20E+04  
- d) 5.56E+04  
- e) 5.95E+04  
===8===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 9xy\hat x +  5.4y^3\hat y </math>, along the y axis from  y = 3 to y = 19}
- a) 1.54E+05  
- b) 1.64E+05  
+ c) 1.76E+05  
- d) 1.88E+05  
- e) 2.01E+05  
===9===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 7.9xy\hat x +  9.7y^3\hat y </math>, along the y axis from  y = 3 to y = 18}
- a) 1.94E+05  
- b) 2.08E+05  
- c) 2.22E+05  
- d) 2.38E+05  
+ e) 2.54E+05  
===10===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 6.1xy\hat x +  5.9y^3\hat y </math>, along the y axis from  y = 6 to y = 12}
+ a) 2.87E+04  
- b) 3.07E+04  
- c) 3.28E+04  
- d) 3.51E+04  
- e) 3.76E+04  
===11===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 6.8xy\hat x +  7y^3\hat y </math>, along the y axis from  y = 3 to y = 17}
- a) 1.28E+05  
- b) 1.36E+05  
+ c) 1.46E+05  
- d) 1.56E+05  
- e) 1.67E+05  
===12===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 9.9xy\hat x +  6.1y^3\hat y </math>, along the y axis from  y = 7 to y = 16}
- a) 7.86E+04  
- b) 8.41E+04  
- c) 9.00E+04  
+ d) 9.63E+04  
- e) 1.03E+05  
===13===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 6.9xy\hat x +  7.4y^3\hat y </math>, along the y axis from  y = 3 to y = 18}
- a) 1.69E+05  
- b) 1.81E+05  
+ c) 1.94E+05  
- d) 2.08E+05  
- e) 2.22E+05  
===14===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 8.3xy\hat x +  8.6y^3\hat y </math>, along the y axis from  y = 4 to y = 16}
- a) 1.31E+05  
+ b) 1.40E+05  
- c) 1.50E+05  
- d) 1.61E+05  
- e) 1.72E+05  
===15===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 8.9xy\hat x +  5.4y^3\hat y </math>, along the y axis from  y = 7 to y = 17}
+ a) 1.10E+05  
- b) 1.17E+05  
- c) 1.25E+05  
- d) 1.34E+05  
- e) 1.44E+05  
===16===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 9.4xy\hat x +  9.3y^3\hat y </math>, along the y axis from  y = 6 to y = 18}
- a) 2.11E+05  
- b) 2.25E+05  
+ c) 2.41E+05  
- d) 2.58E+05  
- e) 2.76E+05  
===17===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 6.9xy\hat x +  5.5y^3\hat y </math>, along the y axis from  y = 7 to y = 18}
+ a) 1.41E+05  
- b) 1.51E+05  
- c) 1.61E+05  
- d) 1.73E+05  
- e) 1.85E+05  
===18===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 8.4xy\hat x +  8.3y^3\hat y </math>, along the y axis from  y = 5 to y = 15}
- a) 9.70E+04  
+ b) 1.04E+05  
- c) 1.11E+05  
- d) 1.19E+05  
- e) 1.27E+05  
===19===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 7.3xy\hat x +  5.2y^3\hat y </math>, along the y axis from  y = 5 to y = 11}
+ a) 1.82E+04  
- b) 1.95E+04  
- c) 2.09E+04  
- d) 2.23E+04  
- e) 2.39E+04  
===20===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 7.8xy\hat x +  8y^3\hat y </math>, along the y axis from  y = 6 to y = 13}
- a) 4.45E+04  
- b) 4.76E+04  
- c) 5.10E+04  
+ d) 5.45E+04  
- e) 5.83E+04  
===21===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, <math>\vec F = 8.5xy\hat x +  7.5y^3\hat y </math>, along the y axis from  y = 7 to y = 18}
- a) 1.68E+05  
- b) 1.80E+05  
+ c) 1.92E+05  
- d) 2.06E+05  
- e) 2.20E+05  
</pre>
{{cob}}
==a07energy_lineIntegral_2_v1==
<quiz display="simple">
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^7\theta^9\hat r + r^7\theta^ 5\hat \theta</math> , along the first quadrant of a circle of radius 8}
- a) 3.43E+07 
- b) 3.67E+07 
- c) 3.93E+07 
+ d) 4.20E+07 
- e) 4.49E+07 
</quiz>
{{cot|copies}}
<pre>
===2===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^6\theta^8\hat r + r^7\theta^ 6\hat \theta</math> , along the first quadrant of a circle of radius 5}
- a) 1.15E+06 
- b) 1.23E+06 
+ c) 1.32E+06 
- d) 1.41E+06 
- e) 1.51E+06 
===3===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^6\theta^6\hat r + r^8\theta^ 7\hat \theta</math> , along the first quadrant of a circle of radius 3}
- a) 6.96E+04 
- b) 7.44E+04 
- c) 7.97E+04 
- d) 8.52E+04 
+ e) 9.12E+04 
===4===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^4\theta^6\hat r + r^7\theta^ 8\hat \theta</math> , along the first quadrant of a circle of radius 6}
+ a) 1.09E+07 
- b) 1.16E+07 
- c) 1.24E+07 
- d) 1.33E+07 
- e) 1.42E+07 
===5===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^8\theta^9\hat r + r^8\theta^ 5\hat \theta</math> , along the first quadrant of a circle of radius 6}
- a) 2.06E+07 
- b) 2.20E+07 
- c) 2.36E+07 
+ d) 2.52E+07 
- e) 2.70E+07 
===6===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^7\theta^8\hat r + r^9\theta^ 4\hat \theta</math> , along the first quadrant of a circle of radius 8}
- a) 1.68E+09 
- b) 1.79E+09 
- c) 1.92E+09 
+ d) 2.05E+09 
- e) 2.20E+09 
===7===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^9\theta^3\hat r + r^8\theta^ 7\hat \theta</math> , along the first quadrant of a circle of radius 4}
- a) 1.14E+06 
+ b) 1.21E+06 
- c) 1.30E+06 
- d) 1.39E+06 
- e) 1.49E+06 
===8===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^5\theta^7\hat r + r^4\theta^ 4\hat \theta</math> , along the first quadrant of a circle of radius 9}
- a) 1.06E+05 
+ b) 1.13E+05 
- c) 1.21E+05 
- d) 1.29E+05 
- e) 1.38E+05 
===9===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^3\theta^4\hat r + r^6\theta^ 5\hat \theta</math> , along the first quadrant of a circle of radius 9}
- a) 1.12E+07 
+ b) 1.20E+07 
- c) 1.28E+07 
- d) 1.37E+07 
- e) 1.47E+07 
===10===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^4\theta^3\hat r + r^6\theta^ 7\hat \theta</math> , along the first quadrant of a circle of radius 7}
- a) 3.33E+06 
- b) 3.57E+06 
+ c) 3.82E+06 
- d) 4.08E+06 
- e) 4.37E+06 
===11===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^3\theta^7\hat r + r^7\theta^ 4\hat \theta</math> , along the first quadrant of a circle of radius 4}
- a) 1.02E+05 
- b) 1.09E+05 
- c) 1.17E+05 
+ d) 1.25E+05 
- e) 1.34E+05 
===12===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^5\theta^4\hat r + r^5\theta^ 8\hat \theta</math> , along the first quadrant of a circle of radius 5}
- a) 8.25E+04 
- b) 8.83E+04 
- c) 9.45E+04 
+ d) 1.01E+05 
- e) 1.08E+05 
===13===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^6\theta^8\hat r + r^8\theta^ 9\hat \theta</math> , along the first quadrant of a circle of radius 3}
- a) 1.37E+05 
- b) 1.47E+05 
- c) 1.57E+05 
- d) 1.68E+05 
+ e) 1.80E+05 
===14===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^8\theta^5\hat r + r^4\theta^ 6\hat \theta</math> , along the first quadrant of a circle of radius 4}
- a) 2.63E+03 
- b) 2.82E+03 
- c) 3.01E+03 
- d) 3.23E+03 
+ e) 3.45E+03 
===15===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^5\theta^3\hat r + r^6\theta^ 6\hat \theta</math> , along the first quadrant of a circle of radius 3}
- a) 6.44E+03 
- b) 6.89E+03 
+ c) 7.37E+03 
- d) 7.89E+03 
- e) 8.44E+03 
===16===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^7\theta^4\hat r + r^5\theta^ 6\hat \theta</math> , along the first quadrant of a circle of radius 7}
- a) 3.03E+05 
- b) 3.24E+05 
- c) 3.46E+05 
- d) 3.71E+05 
+ e) 3.97E+05 
===17===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^9\theta^6\hat r + r^4\theta^ 4\hat \theta</math> , along the first quadrant of a circle of radius 7}
- a) 2.45E+04 
- b) 2.62E+04 
- c) 2.81E+04 
- d) 3.00E+04 
+ e) 3.21E+04 
===18===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^9\theta^4\hat r + r^7\theta^ 8\hat \theta</math> , along the first quadrant of a circle of radius 8}
- a) 8.86E+07 
- b) 9.48E+07 
- c) 1.01E+08 
+ d) 1.09E+08 
- e) 1.16E+08 
===19===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^9\theta^5\hat r + r^8\theta^ 7\hat \theta</math> , along the first quadrant of a circle of radius 4}
- a) 1.14E+06 
+ b) 1.21E+06 
- c) 1.30E+06 
- d) 1.39E+06 
- e) 1.49E+06 
===20===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^7\theta^3\hat r + r^4\theta^ 7\hat \theta</math> , along the first quadrant of a circle of radius 3}
- a) 1.05E+03 
+ b) 1.13E+03 
- c) 1.20E+03 
- d) 1.29E+03 
- e) 1.38E+03 
===21===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, <math>\vec F = r^6\theta^5\hat r + r^9\theta^ 7\hat \theta</math> , along the first quadrant of a circle of radius 3}
- a) 2.09E+05 
- b) 2.23E+05 
- c) 2.39E+05 
- d) 2.56E+05 
+ e) 2.74E+05 
</pre>
{{cob}}
==a07energy_lineIntegral_3_v1==
<quiz display="simple">
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 4xy\hat x +  7.7x\hat y </math>  from the origin to the point at x = 2.5 and y = 3.3}
+ a) 5.93E+01 
- b) 6.34E+01 
- c) 6.78E+01 
- d) 7.26E+01 
- e) 7.77E+01 
</quiz>
{{cot|copies}}
<pre>
===2===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 3xy\hat x +  6.9x\hat y </math>  from the origin to the point at x = 2.3 and y = 3.8}
- a) 4.70E+01 
+ b) 5.03E+01 
- c) 5.38E+01 
- d) 5.75E+01 
- e) 6.16E+01 
===3===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 2.9xy\hat x +  7.3x\hat y </math>  from the origin to the point at x = 2.3 and y = 3.8}
- a) 4.48E+01 
- b) 4.80E+01 
+ c) 5.13E+01 
- d) 5.49E+01 
- e) 5.88E+01 
===4===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 1.3xy\hat x +  6.4x\hat y </math>  from the origin to the point at x = 2.2 and y = 3.6}
- a) 3.07E+01 
+ b) 3.29E+01 
- c) 3.52E+01 
- d) 3.77E+01 
- e) 4.03E+01 
===5===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 2.6xy\hat x +  8.6x\hat y </math>  from the origin to the point at x = 2.9 and y = 3.7}
+ a) 7.31E+01 
- b) 7.82E+01 
- c) 8.37E+01 
- d) 8.96E+01 
- e) 9.58E+01 
===6===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 4xy\hat x +  9.8x\hat y </math>  from the origin to the point at x = 2.6 and y = 3.9}
- a) 7.93E+01 
+ b) 8.48E+01 
- c) 9.08E+01 
- d) 9.71E+01 
- e) 1.04E+02 
===7===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 3.8xy\hat x +  5.1x\hat y </math>  from the origin to the point at x = 2.5 and y = 3.2}
- a) 4.27E+01 
+ b) 4.57E+01 
- c) 4.89E+01 
- d) 5.24E+01 
- e) 5.60E+01 
===8===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 1.6xy\hat x +  8x\hat y </math>  from the origin to the point at x = 2.6 and y = 3.4}
+ a) 4.76E+01 
- b) 5.10E+01 
- c) 5.45E+01 
- d) 5.83E+01 
- e) 6.24E+01 
===9===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 1.2xy\hat x +  5.3x\hat y </math>  from the origin to the point at x = 2.1 and y = 3.1}
- a) 1.73E+01 
- b) 1.85E+01 
- c) 1.98E+01 
- d) 2.12E+01 
+ e) 2.27E+01 
===10===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 3.3xy\hat x +  8.7x\hat y </math>  from the origin to the point at x = 2.1 and y = 3.2}
- a) 4.18E+01 
+ b) 4.48E+01 
- c) 4.79E+01 
- d) 5.12E+01 
- e) 5.48E+01 
===11===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 3.8xy\hat x +  9.8x\hat y </math>  from the origin to the point at x = 2.9 and y = 3.4}
- a) 7.90E+01 
+ b) 8.45E+01 
- c) 9.05E+01 
- d) 9.68E+01 
- e) 1.04E+02 
===12===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 1.6xy\hat x +  8.7x\hat y </math>  from the origin to the point at x = 2.7 and y = 3.2}
- a) 4.37E+01 
- b) 4.68E+01 
+ c) 5.00E+01 
- d) 5.35E+01 
- e) 5.73E+01 
===13===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 1.2xy\hat x +  8.3x\hat y </math>  from the origin to the point at x = 2.8 and y = 3.8}
- a) 4.58E+01 
- b) 4.90E+01 
- c) 5.24E+01 
+ d) 5.61E+01 
- e) 6.00E+01 
===14===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 2.4xy\hat x +  6.8x\hat y </math>  from the origin to the point at x = 2.1 and y = 3.8}
+ a) 4.05E+01 
- b) 4.34E+01 
- c) 4.64E+01 
- d) 4.97E+01 
- e) 5.31E+01 
===15===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 1.1xy\hat x +  6.4x\hat y </math>  from the origin to the point at x = 2.9 and y = 3.7}
- a) 4.28E+01 
+ b) 4.57E+01 
- c) 4.89E+01 
- d) 5.24E+01 
- e) 5.60E+01 
===16===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 3.7xy\hat x +  8.4x\hat y </math>  from the origin to the point at x = 2.6 and y = 3.4}
- a) 5.00E+01 
- b) 5.34E+01 
- c) 5.72E+01 
- d) 6.12E+01 
+ e) 6.55E+01 
===17===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 3.6xy\hat x +  5.1x\hat y </math>  from the origin to the point at x = 2.2 and y = 3.5}
- a) 3.49E+01 
- b) 3.73E+01 
+ c) 4.00E+01 
- d) 4.28E+01 
- e) 4.58E+01 
===18===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 2xy\hat x +  7.2x\hat y </math>  from the origin to the point at x = 2.4 and y = 3.2}
- a) 3.05E+01 
- b) 3.26E+01 
- c) 3.49E+01 
- d) 3.73E+01 
+ e) 3.99E+01 
===19===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 2.2xy\hat x +  9.2x\hat y </math>  from the origin to the point at x = 2.1 and y = 3.4}
+ a) 4.38E+01 
- b) 4.69E+01 
- c) 5.02E+01 
- d) 5.37E+01 
- e) 5.75E+01 
===20===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 2xy\hat x +  9.7x\hat y </math>  from the origin to the point at x = 2.8 and y = 3.2}
- a) 5.26E+01 
- b) 5.62E+01 
+ c) 6.02E+01 
- d) 6.44E+01 
- e) 6.89E+01 
===21===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of <math>\vec F = 2xy\hat x +  9.5x\hat y </math>  from the origin to the point at x = 2.1 and y = 3.8}
+ a) 4.91E+01 
- b) 5.25E+01 
- c) 5.62E+01 
- d) 6.01E+01 
- e) 6.43E+01 
</pre>
{{cob}}
==a07energy_lineIntegral_4_v1==
<quiz display="simple">
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^2y^2\hat x + x^2y^3\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 4.45E-01  
- b) 4.76E-01  
- c) 5.10E-01  
- d) 5.45E-01  
+ e) 5.83E-01  
</quiz>
{{cot|copies}}
<pre>
===2===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^2y^3\hat x + x^2y^4\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 4.66E-01  
- b) 4.98E-01  
+ c) 5.33E-01  
- d) 5.71E-01  
- e) 6.11E-01  
===3===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^3y^5\hat x + x^2y^3\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.81E-01  
- b) 4.08E-01  
- c) 4.37E-01  
- d) 4.67E-01  
+ e) 5.00E-01  
===4===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^5y^2\hat x + x^5y^3\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.64E-01  
- b) 3.89E-01  
+ c) 4.17E-01  
- d) 4.46E-01  
- e) 4.77E-01  
===5===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^4y^4\hat x + x^5y^4\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.27E-01  
- b) 3.49E-01  
- c) 3.74E-01  
+ d) 4.00E-01  
- e) 4.28E-01  
===6===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^3y^5\hat x + x^5y^2\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 4.76E-01  
- b) 5.10E-01  
- c) 5.45E-01  
+ d) 5.83E-01  
- e) 6.24E-01  
===7===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^5y^4\hat x + x^5y^4\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
+ a) 3.67E-01  
- b) 3.92E-01  
- c) 4.20E-01  
- d) 4.49E-01  
- e) 4.81E-01  
===8===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^4y^5\hat x + x^3y^3\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 4.21E-01  
+ b) 4.50E-01  
- c) 4.82E-01  
- d) 5.15E-01  
- e) 5.51E-01  
===9===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^5y^3\hat x + x^5y^4\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.43E-01  
+ b) 3.67E-01  
- c) 3.92E-01  
- d) 4.20E-01  
- e) 4.49E-01  
===10===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^2y^2\hat x + x^4y^3\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 5.10E-01  
- b) 5.45E-01  
+ c) 5.83E-01  
- d) 6.24E-01  
- e) 6.68E-01  
===11===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^2y^5\hat x + x^2y^4\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
+ a) 5.33E-01  
- b) 5.71E-01  
- c) 6.11E-01  
- d) 6.53E-01  
- e) 6.99E-01  
===12===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^3y^4\hat x + x^4y^4\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.43E-01  
- b) 3.67E-01  
- c) 3.93E-01  
- d) 4.21E-01  
+ e) 4.50E-01  
===13===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^2y^4\hat x + x^4y^5\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 4.08E-01  
- b) 4.37E-01  
- c) 4.67E-01  
+ d) 5.00E-01  
- e) 5.35E-01  
===14===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^5y^2\hat x + x^2y^4\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.43E-01  
+ b) 3.67E-01  
- c) 3.92E-01  
- d) 4.20E-01  
- e) 4.49E-01  
===15===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^4y^2\hat x + x^4y^5\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
+ a) 3.67E-01  
- b) 3.92E-01  
- c) 4.20E-01  
- d) 4.49E-01  
- e) 4.81E-01  
===16===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^3y^2\hat x + x^2y^4\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.43E-01  
- b) 3.67E-01  
- c) 3.93E-01  
- d) 4.21E-01  
+ e) 4.50E-01  
===17===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^4y^2\hat x + x^3y^4\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.74E-01  
+ b) 4.00E-01  
- c) 4.28E-01  
- d) 4.58E-01  
- e) 4.90E-01  
===18===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^2y^4\hat x + x^4y^3\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 5.10E-01  
- b) 5.45E-01  
+ c) 5.83E-01  
- d) 6.24E-01  
- e) 6.68E-01  
===19===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^4y^2\hat x + x^2y^3\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
+ a) 4.50E-01  
- b) 4.82E-01  
- c) 5.15E-01  
- d) 5.51E-01  
- e) 5.90E-01  
===20===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^5y^5\hat x + x^5y^5\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.12E-01  
+ b) 3.33E-01  
- c) 3.57E-01  
- d) 3.82E-01  
- e) 4.08E-01  
===21===
{<!--a07energy_lineIntegral_4-->Integrate the function, <math>\vec F = -x^3y^2\hat x + x^5y^3\hat y</math>, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
+ a) 5.00E-01  
- b) 5.35E-01  
- c) 5.72E-01  
- d) 6.13E-01  
- e) 6.55E-01  
</pre>
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