Homework Help: Triple integration over portion of Sphere

1. Oct 4, 2016

nysnacc

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

2. Relevant equations
spherical Jacobean

3. The attempt at a solution
I have (sorry, have to capture my work, too hard to type)

then the integration of p3 ep2 = 1/2 ep2 (p2-3/2) ??

2. Oct 4, 2016

nysnacc

The answer I got using cylindrical was eπ/8,
but here, using the spherical, I got π(e+3)/64

3. Oct 4, 2016

Ray Vickson

No. You can check that for yourself, by showing that the derivative is not $r^3 \exp(r^2)$.

Do integration by parts.

BTW: I get $\pi/8$ using spherical coordinates.

4. Oct 4, 2016

nysnacc

π/8 not πe/8 ?

5. Oct 4, 2016

Ray Vickson

I wrote exactly what I meant.

If you had a different upper bound of $r = a$ instead of $r = 1$ you would, indeed, get an exponential in the answer.