# find the area bound by curves y=ex , y=lnx,its assumtodes and the curve x2+y2-2x-2y+1=0 .

Jitender Singh IIT Delhi
8 years ago
Ans:
We need to find the area of the region common to following five curves:
$y = e^x$
$y = lnx$
$y = 0$
$x = 0$
$(x-1)^2+ (y-1)^2 = 1$
From the diagram, it is clear that tha area of region ‘A’ is:
$A = \int_{0}^{1}1-\sqrt{1-(x-1)^{2}}dx$
$A = (x-(\frac{(x-1)}{2}.\sqrt{1-(x-1)^{2}}+\frac{1}{2}.sin^{-1}(x-1)))_{0}^{1}$
$A = 1- \frac{\pi }{4}$
Thanks & Regards
Jitender Singh
IIT Delhi