Question

Calculate Volume of $S:= \{(x,y,z) \in \Bbb R^3 \mid z\gt 0, a^2 \lt x^2+y^2+z^2 \lt b^2, z^2 \lt c^2(x^2+y^2) \}$

score 34 · Answer 1 · 2017-01-28 15:33:02

34

Views

Calculate Volume of $S:= \{(x,y,z) \in \Bbb R^3 \mid z\gt 0, a^2 \lt x^2+y^2+z^2 \lt b^2, z^2 \lt c^2(x^2+y^2) \}$

Published on 28 Jan 2017 - 15:33

score 50 · Answer 2 · 2017-01-29 09:56:28

50

Views

Show: $U(y):=\int {\frac{f(\mid x \mid)}{\mid x-y \mid }dx}=\frac{\int {f(\mid x \mid)dx}}{\mid y\mid}$

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score 230 · Answer 3 · 2017-01-29 16:56:13

230

Views

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90

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357

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44

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score 233 · Answer 15 · 2017-02-12 13:47:02

233

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List Question

Calculate Volume of $S:= \{(x,y,z) \in \Bbb R^3 \mid z\gt 0, a^2 \lt x^2+y^2+z^2 \lt b^2, z^2 \lt c^2(x^2+y^2) \}$

Show: $U(y):=\int {\frac{f(\mid x \mid)}{\mid x-y \mid }dx}=\frac{\int {f(\mid x \mid)dx}}{\mid y\mid}$

Change of variables notation clarification

General solution of particular first-order nonlinear PDE

Computing differential operator after change of coordinates

Help with volume calculation via change of variables

Change of variables in Heat Equation (and Fourier Series)

How to apply change of variables to identity map?

Confusion about normal of sphere using parametrization

Why can't change of variables be done using the density distribution?

Can indefinite double integrals be solved by change of variables technique?

Reparameterization of hyperprior distribution

Multivariable calculus chain rule and change of variables

Change of variables for $\int_M \sqrt{u + v} d\lambda^2$

Multidimensional Integral by Change of Variable

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