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Evaluate the triple integral of


over the the solid cylinder with height $4$ and with base of radius $1$ centered on the $z$-axis at $z=−3$.

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Fine, you've already asked one about spherical coordinates like this. Since you're new on Math.SE I think it's good to tell you something: when you post something here we expect to see some argument around what have you tried. If you're trying to get started and you are lost, that's fine, we can help. But tell that and ask just one exercise to get an example. If you don't try thinking by yourself you won't learn math. – user1620696 Mar 24 '13 at 22:47
up vote 2 down vote accepted

In this case, the integral only depends on the cylindrical radial coordinate, so it easily becomes a single integral:

$$2 \pi 4 \int_0^1 dr \,r \sin{r^2} = 4 \pi \int_0^1 du \: \sin{u} = 4 \pi (1-\cos{1}) $$

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Thanks. Im starting to get the hang of this. – Michael Rametta Mar 26 '13 at 0:43

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