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

I have this question about triple integrals and spherical coordinates

2. Relevant equations

y = sin sin

x = sin cos

z = cos

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

Thus I need to find the limits of integration for and

3. The attempt at a solution

I used the limits for the z to obtain z^2.

Thus, z^2 + x^2+y^2 = 4

Using the identity for ^2 = z^2 + y^2 + x^2 then ^2 = 4

which gives me a value of = 2.

To get I graphed the x limits of the integral. Since x = then x^2 + y ^2 =4. Therefore it is a circle of radius 2. Thus I assumed that goes from 0 to 2 .

Now my problem is to find the limits for which I don't know how to get.

Any ideas on how to solve for and also, can someone double check that the other limits of integration are correct?

Since z^2^ +y^2 + x^2 = 4 is a sphere and spheres have a from 0 to . Can I use those limits for . Can anybody double check that my limits of integration are correct?

Thank you!