# Homework Help: Solid of revolution (should be simple)

1. Jun 30, 2011

### Paulo Serrano

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

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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 [Broken]

Last edited by a moderator: May 5, 2017
2. Jun 30, 2011

### SammyS

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

3. Jun 30, 2011

### 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

4. Jun 30, 2011

### SammyS

Staff Emeritus
Of course! You're right.

What axis is this area to be revolved around?

5. Jun 30, 2011

### Paulo Serrano

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

It looks kinda similar...but not quite.

6. Jun 30, 2011

### SammyS

Staff Emeritus
Your work looks good to me !!