Find the volume of a solid...Please help!

[nikchic5]

I am studying for a Calc II test so please help me as soon as possible! Thanks so much
Here is the question...
Find the volume of the solid formed by revolving the region bounded by the graphs of the y=e^x , y=0 , x=0 , and x=1 about the y-axis.
I started with V=pi (the intergral from 0 to 1) (e^x)^2

Is that correct? And also could you help me to finish it? Thanks so much!

 

[tkhunny]

It appears that you have it. I would recommend doing it by shells, just for the practice.

\(\displaystyle \L\;\int_{1}^{e}{2*\pi*y*(1-ln(y))}\;dy + \pi*1^{2}*1\)

 

[nikchic5]

Follow up question..

If I do it the way I did it was I correct on the integral or was I supposed to do it from 0 to e?
Because the final answer is pi/2(e^2-1)

by the way it was about the x-axis not the y-axis. Thnaks so much!

 

[tkhunny]

You have the right limits for disks along the x-axis.

Do you need help finding the antiderivative? I hope not. Have a little more confidence! This is one thing that doing it both ways provides. You gain experience and confidence.