Evaluate the triple integral of f(x, y,z)=z(x2+y2+z2)−3/2f(x, y,z)=z(x2+y2+z2)−3/2 over the part of the ball x2+y2+z2≤49x2+y2+z2≤49 defined by z≥3.5z≥3.5. ∫

I'm going to take a wild guess and assume you mean



(as opposed to subtracting 3/2, say)

Convert to spherical coordinates, taking



Now when , below the "cap" of the ball we have a right triangle with hypotenuse coinciding with the ball's radius and a leg of length , with the angle between them satisfying



Furthermore, when , we have



Call the cap . Then the triple integral over is

There are no table and graph present in this problem