Question

How to calculate $\int_{x^2+y^2+z^2\leq R^2}\frac{dxdydz}{\sqrt{(x-a)^2+(y-b)^2+(z-c)^2}}$, where $a^2+b^2+c^2>R^2$?

score 74 · Answer 1 · 2023-08-23 08:08:39

74

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How to calculate $\int_{x^2+y^2+z^2\leq R^2}\frac{dxdydz}{\sqrt{(x-a)^2+(y-b)^2+(z-c)^2}}$, where $a^2+b^2+c^2>R^2$?

Published on 23 Aug 2023 - 8:08

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50

Views

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121

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List Question

How to calculate $\int_{x^2+y^2+z^2\leq R^2}\frac{dxdydz}{\sqrt{(x-a)^2+(y-b)^2+(z-c)^2}}$, where $a^2+b^2+c^2>R^2$?

How to change constant bounds in double integral into polar.

nature of a triple integrale

Finding $P(X+Y<1)$ given $f(x,y) = 12xy^3$ when $0 < x < y < 1$

Is there any integrable function in two variables such that it is integrable for any fixed $y$ but the iterated integral does not exist?

Calculate the volume of the body defined by $x^2+y^2+z^2≤1$ for which $x^2+z^2≥z$

Algebraic manipulation of the product of multiple differentials

Solving double integrals of sin and cosine using Fourier integral theorem

Evaluate double integral (find square of areas)

Why is this domain wrong?

Integral inequality from AMM 1992

Double integral giving different results after changing order of integration

The moment of inertia: limits for angles.

Mass of an ellipsoid with variable density

Double integral and existence of limit

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