# Help with volume of solid of revolution/integration by parts question

1. Feb 12, 2014

### student93

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

The problem is attached in this post.

2. Relevant equations

The problem is attached in this post.

3. The attempt at a solution

I've set up the integral via disk method: π∫(e^√x)^2 dx from 0 to 1

I've done integration by parts by don't know how to integrate the second term of the integration by parts which is: ∫(xe^2√x)/(√x) dx from 0 to 1

Also the answer to the question is (π/2)(e^2+1)

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2. Feb 12, 2014

### LCKurtz

That problem obviously has a typo in it somewhere. Your integral is correct but it is not an elementary integral and won't match any of the answers.

3. Feb 12, 2014

### student93

I'm pretty sure there's no typo in the question, when I plug in the integral into wolfram alpha, I get the correct answer which is (π/2)(e^2+1)

Last edited: Feb 12, 2014
4. Feb 12, 2014

### PeroK

How did you do the integration by parts? For the integral:

$$\int_0^1 e^{2\sqrt{x}}dx$$

Did you think about a substitution?

5. Feb 12, 2014

### LCKurtz

Yep. I looked at it too quickly. Try $2\sqrt x = \ln u$ on it.

6. Feb 12, 2014

### student93

u=e^(2√x) dv=dx
du=(e^(2√x))/(√x) dx v=x

∫e^(2√x)dx = xe^(2√x) - ∫((xe^(2√x))/(√x)

7. Feb 12, 2014

### PeroK

I think parts was the wrong way to go. What about the obvious substitution u = √x? In the original integral.

8. Feb 12, 2014

### student93

I don't think u-substitution works in this case, also the directions specifically ask to solve the question via integration by parts.

Also here's the original integral:

π∫e^(2√x) dx, from 0 to 1

9. Feb 12, 2014

### PeroK

The u-substitution does work. It simplifies things ready for the integration by parts!

10. Feb 12, 2014

### LCKurtz

Substitution does work. Try one of the substitutions that have been suggested and you will see.

11. Feb 12, 2014

### student93

Could you please show exactly how you would do the u-substitution before doing integration by parts? I want to make sure I understand this concept etc.

12. Feb 12, 2014