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## Homework Statement

Let A be the region that in space bounded by the balls:

[tex] x^2 +y^2 + z^2 =1 [/tex] , [tex] x^2 +y^2 +z^2 =4 [/tex] , above the plane [tex]z=0[/tex] and inside the cone [tex]z^2 = x^2 +y^2 [/tex].

A. Write the integral [tex] \int \int \int_{A} f(x,y,z) dxdydz [/tex] in the form:

[tex] \int \int_{E} (\int_{g^1(x,y)}^{g^2(x,y)} f(x,y,z) dz) dxdy [/tex] when :

[tex] A=( (x,y,z) | (x,y) \in E, g^1(x,y) \le z \le g^2(x,y) ) [/tex] ...

B. Find the volume of A (not necessarily using part A).

Hope you'll be able to help me in this... I think the main problem is that I can't figure out how A looks like... There is also a hint that one of the functions g1 or g2 should be defined at a split region... I can't figure out how this cone looks like and how I can describe A as equations ...

Thanks in advance!