Question

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

score 1k · Answer 1 · 2026-03-20 13:17:02

1k

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

Published on 20 Mar 2026 - 13:17

score 491 · Answer 2 · 2026-03-20 02:42:59

491

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Undo a change of variables

Published on 20 Mar 2026 - 2:42

score 726 · Answer 3 · 2026-03-19 22:46:04

726

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Optimization problem "change of variables" injectivity requirement

Published on 19 Mar 2026 - 22:46

score 207 · Answer 4 · 2026-03-22 08:42:54

207

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Volume of revolution with coordinate transformation.

Published on 22 Mar 2026 - 8:42

score 175 · Answer 5 · 2026-03-22 08:44:49

175

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

Published on 22 Mar 2026 - 8:44

score 40 · Answer 6 · 2026-03-20 06:37:36

40

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Does the following change of variable hold?

Published on 20 Mar 2026 - 6:37

score 209 · Answer 7 · 2026-03-22 03:20:45

209

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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 22 Mar 2026 - 3:20

score 129 · Answer 8 · 2026-03-22 12:02:58

129

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

Published on 22 Mar 2026 - 12:02

score 72 · Answer 9 · 2026-03-20 03:26:35

72

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

Published on 20 Mar 2026 - 3:26

score 3k · Answer 10 · 2026-03-21 00:45:49

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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 21 Mar 2026 - 0:45

score 37 · Answer 11 · 2026-03-22 23:37:43

37

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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 22 Mar 2026 - 23:37

score 498 · Answer 12 · 2026-03-22 22:14:31

498

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Second order partial derivative chain rule?

Published on 22 Mar 2026 - 22:14

score 757 · Answer 13 · 2026-03-23 00:08:26

757

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Integrating a Delta Function Over a Hypersphere

Published on 23 Mar 2026 - 0:08

score 39 · Answer 14 · 2026-03-23 14:57:07

39

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How to carry out this change of variable?

Published on 23 Mar 2026 - 14:57

score 186 · Answer 15 · 2026-03-23 11:23:01

186

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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 23 Mar 2026 - 11:23

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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