Question
Evaluate the iterated integral.$$\int_{0}^{2} \int_{0}^{\sqrt{4-x^{2}}} \int_{-5+x^{2}+y^{2}}^{3-x^{2}-y^{2}} x d z d y d x$$
Step 1
The integral of $x$ with respect to $z$ is $xz$. We evaluate this from $z=-5+x^{2}+y^{2}$ to $z=3-x^{2}-y^{2}$: $$ \int_{0}^{2} \int_{0}^{\sqrt{4-x^{2}}} x(3-x^{2}-y^{2}) - x(-5+x^{2}+y^{2}) dy dx $$ Show more…
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