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

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

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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
askIITians Faculty

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