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Tagged with bounds-of-integration cylindrical-coordinates
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Write triple integral as cylindrical coordinate of given region, confused in determining lower and upper bound.
Given $E$ is a region as follows:
$$E=\left\{0\leq x\leq 1, 0\leq y\leq \sqrt{1-x^2}, \sqrt{x^2+y^2}\leq z\leq \sqrt{2-x^2-y^2}\right\}.$$
Write triple integral
$$\iiint_\limits{E}xydzdydx$$
as triple ...
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How can I find $\iiint\frac{xz}{1+x^2+y^2}\,dz\,dy\,dx$ where $1≤x^2+y^2≤3, 0≤z≤3$?
Compute $$\iiint\frac{xz}{1+x^2+y^2}\,dz\,dy\,dx,$$ where $1≤x^2+y^2≤3, 0≤z≤3$.
I've tried it. But I'm only confused with $\theta$. I think it should be $0$ to $2\pi$, but that'll make the whole ...
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Evaluating $\int_{-4} ^4\int _0 ^{\sqrt{16-x^2}} \int _0 ^{16-x^2-y^2} \sqrt{x^2 + y^2}\,dz\,dy\,dx$
Question: Evaluate the given triple integral with cylindrical coordinates:
$$\int_{-4} ^4\int _0 ^{\sqrt{16-x^2}} \int _0 ^{16-x^2-y^2} \sqrt{x^2 + y^2}\,dz\,dy\,dx$$
My solution (attempt): Upon ...
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