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Question: Is there a way to help Maple evaluate this triple integral?

Question:Is there a way to help Maple evaluate this triple integral?

widmer 28
calculus
November 21 2010
1

This is for a calculus lab.  I need to show my students how to do this with Maple.

 

int(int(int(VectorCalculus[`*`](VectorCalculus[`+`](r^2, VectorCalculus[`*`](r, cos(theta))), r), z = 0 .. sqrt(VectorCalculus[`+`](a^2, VectorCalculus[`-`](r^2)))), r = 0 .. a), theta = 0 .. VectorCalculus[`*`](2, Pi))

It only does the inner integral and gives  int(int(int(VectorCalculus[`*`](VectorCalculus[`+`](r^2, VectorCalculus[`*`](r, cos(theta))), r), z = 0 .. sqrt(VectorCalculus[`+`](a^2, VectorCalculus[`-`](r^2)))), r = 0 .. a), theta = 0 .. VectorCalculus[`*`](2, Pi))

Derive could do this one.  The answer is  (4*pi*a^5)/15 .
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