# Volume by integration

1. Mar 29, 2016

1. The problem statement, all variables and given/known data
I have the attached problem ,and Show my answer and solution,

Can any one point to the mistake I made???

2. Mar 29, 2016

Your calculation looks correct to me. I don't see any obvious errors.

3. Mar 29, 2016

### Ethan Godden

Your work also looks good to me.
The one thing I noticed is the answer from the book would be right if you take the negative away from the 1.

I'm guessing the book has a typo.

4. Mar 30, 2016

### Staff: Mentor

If this is actually the book's answer, it makes no sense without something following ln.

5. Mar 30, 2016

Thanks
Absolutely right, but draw the function, you will see that volume is almost as his answer(using geometry not integration),and that why I am confused.

6. Mar 30, 2016

### Ray Vickson

If you think that the book's answer $\pi (15+8 \ln(4))$ is close to the correct answer you are very much mistaken. The correct answer is yours, except that the approximation $\pi = 3.14$ is way too crude---just leave it as symbolic $\pi$ until it comes time to evaluate the final answer numerically. Look at the following:
$$\begin{array}{rccc} \pi (15 - 8 \ln\,4 )& \doteq & 12.28251236 & \doteq & 12.3 \\ \pi (15 + 8 \ln\,4 ) & \doteq & 81.96526726 & \doteq & 82.0 \\ \pi 15 & \doteq & 47.12388981 & \doteq & 47.1 \end{array}$$

7. Mar 31, 2016