INSTRUCTOR: Evaluate the triple integral from 0 to pi with respect to theta of the integral from 0 to 1 with respect to r of the integral from 0 to 4 with respect to z of the function r times z times sine of theta, then multiplied by r, in that order. Let's note, these are three of three functions here. One of the functions is r squared. One of them is z. And the other is sine theta.

Those are three separate functions. So we can actually rewrite this as the product of thee integrals. So open parentheses, integral from 0 to pi with respect to theta of sine theta close parentheses, open parentheses integral from 0 to 1 with respect to r of r squared close parentheses, open parentheses integral from 0 to 4 dz of the function z. And then close parentheses.

We can find each of these separately quite easily. The first integral is equal to the value of 2, second has a value of 1/3. The third has a value of 8. So multiplying those three values, we see that this triple integral has a value of 16/3.