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Integrate[1, {z, 0, 5}, {x, -Sqrt[ 9 - y^2], Sqrt[ 9 - y^2]} , {y, -3, 3}] 

60 Sqrt[9 - y^2]

How comes I am not getting a number for my final answer? This triple integral should evaluate to an exact number.

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I edited your question for format. Read this. – Hector Oct 16 '13 at 3:25

Modify your code and notice the order of the integrals

Integrate[f[x, y, z], {z, zo, zf}, {x, a[y], b[y]}, {y, yo, yf}]

enter image description here

The first interval in the code {z, zo, zf} corresponds to the last integral.

From your question, it seems that you meant to compute

Integrate[1, {y, -3, 3}, {x, -Sqrt[9 - y^2], Sqrt[9 - y^2]}, {z, 0, 5}]
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Yes you are right! Hmm.. I would have thought it read from inner integral to outer integral but I couldn't be more wrong! – Adam Staples Oct 16 '13 at 2:46
If my answer satisfies you, accept it: press the check mark below the big number the the top left and the check mark should turn green. You can upvote answers you like: check the up arrow on top of the number. Do the same to your other question. You might want to read these FAQ, especially this one. – Hector Oct 16 '13 at 3:06

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