1. ## Density Function

Seeds are dispersed from a tree in all directions uniformly. The density of seeds that land on the ground at a distance r away is approximately described by the function: s(r) = 50 sin (pi*r/10) seeds/m^2 , 0=<r=<10m

a) At what distance from the tree are the seeds most densely distributed?
b) What is the total number of seeds on the ground within a 10 m radius of the tree?

For part a, I got 5m and for part b, I got 100pi^2. I have a final exam tomorrow and I desperately want to make sure I'm doing this correctly.
Thanks!

2. You are correct on the first part.

For the second part, you need to integrate the density over the entire circular area. Since it is presented in polar coordinates, remember that you should use $\displaystyle r \, dr \, d\theta$.

So:

$\displaystyle \int_0^{2\pi} \int_0^{10} 50 \sin \left( \frac{\pi r}{10} \right) r \, dr \, d\theta$

This gives a different answer than you gave. Is this how you set your integral up? If not, does this make sense why this is correct?