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sachin nayak Grade: 12
        

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

7 years ago

Answers : (1)

Jitender Singh
IIT Delhi
askIITians Faculty
158 Points
										
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

3 years ago
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