Question

Determine the area of the region bounded by the given set of curves. x=e^y, x=1, y=1 and y=2

Answer 1

$x=e^y,x=1,y=1,y=2$

Area under curve is $A=\int_a^bf(x) dx$

$y=1,y=2,x=1$

$F(x)\Rightarrow x=e^y\Rightarrow y=ln(x)$

Area $A=\int_1^2 ln(x)dx$

     

   $=[xln|x|-x]_1^2 \\ =[2ln|2|-2-(1ln|1|-1)] \\ =2ln|2|-2+1 \\ =2\times 0.693-1=0.386$