# Volume by integration

## Homework Statement

I have the attached problem ,and Show my answer and solution,

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

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Homework Helper
Gold Member
Your calculation looks correct to me. I don't see any obvious errors.

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.

Mark44
Mentor
If this is actually the book's answer, it makes no sense without something following ln.

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.

Ray Vickson
Homework Helper
Dearly Missed
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.
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:
$$\begin{array}{rccc} \pi (15 - 8 \ln\,4 )& \doteq & 12.28251236 & \doteq & 12.3 \\ \pi (15 + 8 \ln\,4 ) & \doteq & 81.96526726 & \doteq & 82.0 \\ \pi 15 & \doteq & 47.12388981 & \doteq & 47.1 \end{array}$$

$$\begin{array}{rccc} \pi (15 - 8 \ln\,4 )& \doteq & 12.28251236 & \doteq & 12.3 \\ \pi (15 + 8 \ln\,4 ) & \doteq & 81.96526726 & \doteq & 82.0 \\ \pi 15 & \doteq & 47.12388981 & \doteq & 47.1 \end{array}$$