from matplotlib.pyplot import *
from numpy import linspace, arange
from matplotlib.patches import Polygon

rcParams['font.size'] = 15
rcParams['text.usetex'] = True

x1 = linspace(0,9,100)
y1 = 1./x1
x2 = linspace(1,8,8)
y2 = 1./x2
x3 = arange(1,6,0.01)
y3 = 1./x3
verts = [(1.,0)] + [*zip(x3,y3)] + [(6,0)]
poly = Polygon(verts, facecolor='orange',edgecolor='k')

fig = figure(figsize=(5,5))
ax = fig.add_subplot(111)
ax.grid(True)
ax.plot(x1,y1)
ax.plot(x2,y2,'ro')
ax.add_patch(poly)
ax.text(1,1,r"$\displaystyle f(x)=\frac{1}{x}$", fontdict={'size':20})
ax.text(1.5,.05,r"$\displaystyle\int_1^6f(x)\mathrm{d}x$", fontdict={'size':20})

ax.set_ylim(0,1.2)
ax.set_yticks(linspace(0,1,6))
ax.minorticks_on()
ax.set_xlabel("x", fontsize=18)
ax.set_ylabel("y", fontsize=18)

fig.savefig("1_over_x_integral.svg",bbox_inches="tight",\
	pad_inches=.15)