find the volume of the solid formed by revolving the region bounded by y=e^x, y=0, x=o and x=1 about the y axis

Question

by using the shell method, i got

v=2*pi int(o to 1) (x)(e^x) dx

and my teacher said the answer is e/2 but i keep getting a different answer

Are you sure it is to be rotated about the y axis?
Your attempt ends in dx suggesting you are rotating about the x axis.

It would be a relatively easy question if it is rotated about the x axis, but if you rotate about the y axis that would involve the integral of Pi*(ln y)^2 dy from 1 to e

let me know which way it is before I do that difficult question.