Question

Evaluation of $I=\iint_R e^{-(x^2+y^2)} \,dx\,dy$ by change of variable

score 1k · Answer 1 · 2026-04-29 12:16:41

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Evaluation of $I=\iint_R e^{-(x^2+y^2)} \,dx\,dy$ by change of variable

Published on 29 Apr 2026 - 12:16

score 500 · Answer 2 · 2026-04-29 12:55:23

500

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Undo a change of variables

Published on 29 Apr 2026 - 12:55

score 736 · Answer 3 · 2026-05-07 18:59:53

736

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Optimization problem "change of variables" injectivity requirement

Published on 07 May 2026 - 18:59

score 216 · Answer 4 · 2026-04-29 12:54:28

216

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Volume of revolution with coordinate transformation.

Published on 29 Apr 2026 - 12:54

score 182 · Answer 5 · 2026-04-29 12:55:11

182

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$\int_0^1 \int_0^{1-y} \cos\Big( \frac{x-y}{x+y} \Big) \, dx dy$

Published on 29 Apr 2026 - 12:55

score 47 · Answer 6 · 2026-05-05 06:18:47

47

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Does the following change of variable hold?

Published on 05 May 2026 - 6:18

score 216 · Answer 7 · 2026-05-05 04:10:25

216

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Two variables with joint density: Change of variable technique using Jacobian for $U=\min(X,Y)$ and $V=\max(X,Y)$

Published on 05 May 2026 - 4:10

score 137 · Answer 8 · 2026-05-05 04:11:33

137

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Calculate $\int\int_E e^{5x^2+2xy+y^2}dA$

Published on 05 May 2026 - 4:11

score 77 · Answer 9 · 2026-05-07 17:34:58

77

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$X \sim R(0,1)$ and $Y \sim R(0,1)$ , where $X$ and $Y$ are independent.

Published on 07 May 2026 - 17:34

score 3k · Answer 10 · 2026-04-29 12:55:26

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Given that $X,Y$ are independent $N(0,1)$ , show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}}$ are independent $N(0,\frac{1}{4})$

Published on 29 Apr 2026 - 12:55

score 44 · Answer 11 · 2026-05-05 18:27:48

44

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What coordinates should I determine if I want to find the area of a surface determined by a double integral

Published on 05 May 2026 - 18:27

score 502 · Answer 12 · 2026-04-23 00:51:52

502

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Second order partial derivative chain rule?

Published on 23 Apr 2026 - 0:51

score 761 · Answer 13 · 2026-04-22 12:21:39

761

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Integrating a Delta Function Over a Hypersphere

Published on 22 Apr 2026 - 12:21

score 44 · Answer 14 · 2026-04-23 19:31:51

44

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How to carry out this change of variable?

Published on 23 Apr 2026 - 19:31

score 190 · Answer 15 · 2026-04-22 16:59:40

190

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$\frac{\partial^2 u}{\partial x^2}=\frac{\partial^2 u}{\partial t^2}\implies \frac{\partial^2 v}{\partial \xi\partial \eta}=0$

Published on 22 Apr 2026 - 16:59

List Question

Evaluation of $I=\iint_R e^{-(x^2+y^2)} \,dx\,dy$ by change of variable

Undo a change of variables

Optimization problem "change of variables" injectivity requirement

Volume of revolution with coordinate transformation.

$\int_0^1 \int_0^{1-y} \cos\Big( \frac{x-y}{x+y} \Big) \, dx dy$

Does the following change of variable hold?

Two variables with joint density: Change of variable technique using Jacobian for $U=\min(X,Y)$ and $V=\max(X,Y)$

Calculate $\int\int_E e^{5x^2+2xy+y^2}dA$

$X \sim R(0,1)$ and $Y \sim R(0,1)$ , where $X$ and $Y$ are independent.

Given that $X,Y$ are independent $N(0,1)$ , show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}}$ are independent $N(0,\frac{1}{4})$

What coordinates should I determine if I want to find the area of a surface determined by a double integral

Second order partial derivative chain rule?

Integrating a Delta Function Over a Hypersphere

How to carry out this change of variable?

$\frac{\partial^2 u}{\partial x^2}=\frac{\partial^2 u}{\partial t^2}\implies \frac{\partial^2 v}{\partial \xi\partial \eta}=0$

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