Solid of revolution (should be simple)

[Paulo Serrano]

Hey. Thanks in advanced for the help. This site has helped me a lot through the years.

Homework Statement

Find the volume of the solid formed by rotating the area within y=e^x and y=sin x when 0<x<pi

Homework Equations

The Attempt at a Solution

I've tried it like 10 times on the whiteboard, and did it quickly on a sheet of paper so someone call tell me where I'm going wrong...the answer is supposedly pi/8(e^(2pi)-1)

Here's my work. http://min.us/mvfTL55

 

[SammyS]

The anti-derivative if cos(x) is +sin(x), not -sin(x) .

 

[Paulo Serrano]

Are you sure that's where I made my mistake? The reason it became positive (I think) is not that I got the anti-derivative mixed up. It's because the negative sign outside the parenthesis canceled out the one before the pi*integral of cos2x/2

 

[SammyS]

Of course! You're right.

What is the correct answer?

What axis is this area to be revolved around?

 

[Paulo Serrano]

Around the x-axis. answer is pi/8(e^(2pi)-1)

It looks kinda similar...but not quite.

 

[SammyS]

Your work looks good to me !