(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

f(x) is a differentiable function let

[itex]F(t)= \int\int\int_{x^2+y^2+z^2\leq t^2} f(x^2+y^2+z^2) dx dy dz [/itex]

compute F[itex]^{'}[/itex](t)

2. Relevant equations

x=p sin [itex]\phi[/itex] cos[itex]\theta[/itex]

y= p sin [itex]\phi[/itex] sin[itex]\theta[/itex]

z= p cos [itex]\phi[/itex]

spherical bounds 0<p<t 0<[itex]\phi[/itex]<[itex]\Pi[/itex] 0<[itex]\theta[/itex] < 2[itex]\Pi[/itex]

p^2 sin[itex]\phi[/itex] = jacobian determinant

3. The attempt at a solution

carried through the substitution [itex]\int\int\int f(p^2) p^2 sin \phi dp d\phi d\theta[/itex]

dont know how to evaluate [itex]\int[/itex]f(p^2) sin[itex]\phi[/itex] d[itex]\phi[/itex]???

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

2. Relevant equations

3. The attempt at a solution

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

2. Relevant equations

3. The attempt at a solution

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

2. Relevant equations

3. The attempt at a solution

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

2. Relevant equations

3. The attempt at a solution

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

2. Relevant equations

3. The attempt at a solution

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# Triple integral w/ spherical subsitution

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