Numerical Analysis/Romberg Quiz

<quiz>

{$\underset{0}{\overset{3}{\int }}\frac{sin(2x)}{1+x^2}dx$ |type="()"} - -1.2345435 + 0.4761463020 - 0.2345632784 - 0.567894567

{ Romberg Integration is an extrapolation formula of the trapezoidal rule for integration. |type="()"} +TRUE. -FALSE.

{True error in a multiple segment Trapezoidal rule with n segments for an integral $I=\underset{a}{\overset{b}{\int }}f(x)dx$ is |type="()"} + $E_t=\frac{(b-a{)}^3}{12n^2}\frac{\sum _{i=1}^n{f}^{″}({\xi }_i)}{n}$ - $E_t=\frac{(b{)}^3}{11n^2}\frac{\sum _{i=1}^n{f}^{″}({\xi }_i)}{n}$ - $E_t=\frac{(b-a{)}^3}{12n^2}$ - $E_t=\frac{\sum _{i=1}^n{f}^{″}({\xi }_i)}{n}$

{$\underset{0}{\overset{3}{\int }}sin(4x)e^{-2x}dx$ |type="()"} +0.1997146621 -0.1345234567 -0.2345234234 -1.0000000000

{$\underset{0.04}{\overset{1}{\int }}\frac{1}{\sqrt{x}}dx$ |type="()"} -2.6 +1.6 -4.6 -5.6 </quiz>