Hi Everyone,

I'm having a little problem with the following question that I was hoping someone could help me with.

Basically I need to find the triple integral of (9 - x^2 -y^2) over a region, H, using spherical coordinates where H is the solid hemisphere

x^2 + y^2 + z^2 <= 9,

and z>=0.

Now in terms of actually performing the triple integration, I have no problems, it is getting the spherical coordinates that is really bugging me.

H should be in the following form

H = {p,

θ, φ| a<= 0 <= b, α<= θ<= β, c<=φ<=d} Now I know how to find p(really a and b). In this case a = 0 and b = 3. But I don't know how to find c, d, α, and β. I would really need a step-by-step guide (something like "Spherical Coordinates for dummies" ) If anyone could let me know how to do this I would be most grateful. Also, if someone could provide me with another example of the process just to ensure that my grasp on the method is secure, then that would just be gravy. Eg. E is the area that is to be integrated over, where E lies between the spheres x^2 +y^2+z^2 = 1 and x^2 +y^2 +z^2 =4. (here a = 1, b=2) Thanks in advance to anyone who helps.