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Tagged with bounds-of-integration volume
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Calculating Volume of Spherical Cap using triple integral in cylindrical coordinates and spherical coordinates
Given a sphere above of $xy$-plane with center $(0,0,0)$ and radius $2$ (the equation $z=\sqrt{4-x^2-y^2}$). Plane $z=\sqrt{2}$ intersect the sphere.
I want calculate volume of spherical cap (orange ...
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Why does changing integral bounds get me the wrong answer?
Full disclaimer, this is a homework question.
While solving this question, I came upon the integral $$\int_{-r}^{r}\frac{b\tan^{-1}(\theta)}{2}\sqrt{r^2-x^2} dx$$ Proceeding with trig substitution I ...
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An example of computation of volume of body in $R^3$
How would you solve the following exercise: Compute the volume of the body in $R^3$
bounded by the surface $(x^2+y^2)^2=z^2(3x^2+y^2)$ and planes $z=0$ and $z=5$.
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triple integration to find volume
how can I solve this problem I already have the final answer but I don't know how to solve it , the answer for this problem is $(V=8(pi-1/3)$
I tried solving it with this:
$\int_{-2}^2\int_{-\sqrt{4-...
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