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

Jitender Singh
IIT Delhi
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 & RegardsJitender SinghIIT DelhiaskIITians Faculty

3 years ago
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