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## Homework Statement

Convert the following integral to an equivalent integral in spherical coordinates.

Do NOT evaluate the integral.

∫∫∫ r^3 dz dr dtheta

limits of integration

pi/4<theta<pi/2

0<r<2

0<z<√(2r-r^2)

## Homework Equations

z=pcos(theta)

r^2=x^2 +y^2

p^2=x^2 +y^2 +z^2

theta=theta

## The Attempt at a Solution

My problem is not converting the actual integrand but finding the new limits of integration. I realize that the theta limits will stay the same, but I am not sure how to find the rho or phi limits.

I have found through conversions that the new integrand will be

∫∫∫(p^5)sin(phi)^4 dp dphi dtheta