Question
Evaluate the iterated integral.$$\int_{0}^{3} \int_{0}^{\sqrt{9-z^{2}}} \int_{0}^{x} x y d y d x d z$$
Step 1
The integral of $xy$ with respect to $y$ is $\frac{xy^2}{2}$. Evaluating this from $0$ to $x$ gives us $\frac{x^3}{2}$. So, the integral becomes: $$ \int_{0}^{3} \int_{0}^{\sqrt{9-z^{2}}} \frac{x^3}{2} dx dz $$ Show more…
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