Maths Volume Question

Question

I'm having difficulty with solving this question.

Im squaring the e^2x etc and still cannot seem to get the correct answer ?

Any help or pointers greatly appreciated!!

The region bounded by y=e^2x, y=0, x=-1, x=1 is rotated around the x axis. Find the Volume.

Answer 1

squaring e^2x will get you e^4x

then integral of this would get (e^4x)/4

with the limits from -1 to 1, you will get definite integral of (e^4 - e^-4)/4

volume of integral is pi * the definite integral

so the answer would be 13.645*pi or 42.867