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Write down but don't solve the integrals?
Suppose that E is the region in space bounded below by the cone z = sort(x^2+y^2) and above the sphere (x^2+y^2+z^2)=4. Write (but DON'T evaluate) (triple integral)x^2 dV in both spherical and cylindrical coordinates.
I know x=psin(phi)cos(theta)
and 0<p<2
But what are my bounds for Phi and Theta?
1 Answer
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- ?Lv 67 years agoFavorite Answer
z = r
r^2 + z^2 = 4
therefore
z = r & z = sqrt(4 - r^2)
int_0^(2*pi) int_0^sqrt(2) int_sqrt(4 - r^2)^r dz r dr d(theta)
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