Which of the following integrals represents the volume of the solid obtained by

Question

Which of the following integrals represents the volume of the solid obtained by rotating the region bounded by the curves y=ln(x), y=0, and x=2 about the y-axis? List all that apply.

A) The integral bounded from 1 to 2 of 2pi(x)ln(x)dx
B) The integral bounded from 1 to 2 of 2pi(x-2)ln(x)dx
C) The integral bounded from 0 to 2 of 2pi(x-2)ln(x)dx
D) The integral bounded from 0 to 2 of 2pi(ln(x))dx
E) The integral bounded from 1 to 2 of 2pi(ln(x))dx
F) The integral bounded from 0 to 2 of 2pi(x)ln(x)dx

Explanation / Answer

given, y=lnx, y=0 and x=2 and rotating about y-axis

when y=0 , x=e^0=1

Therfore x varies from 1 to 2

by shell method

Volume V=The integral bounded from 1 to 2 of 2pi(x)ln(x)dx ...(A)..........ans

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