You need to evaluate the volume of the solid obtained by the rotation of the region bounded by the curves `y = ln x , y = 1, y = 2,x=0` about y axis, using washer method, such that:
`V = int_a^b (f^2(x) - g^2(x))dx, f(x)>g(x)`
You may evaluate the volume
`V = pi*int_1^2 (e^y - 0^2)^2dy`
`V = pi*int_1^2 e^(2y)dy`
`V = (pi/2)*(e^(2y))|_1^2`
`V = (pi/2)*(e^(2*2) - e^(2*1))`
`V = (pi/2)*(e^4 - e^2)`
Hence, evaluating the volume of the solid obtained by the rotation of the region bounded by the curves `y = ln x , y = 1, y = 2,x=0` about y axis, yields `V = pi*(e^4 - e^2)/2.`
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