Question

Does the Leibniz rule for $\frac{\partial}{\partial x}\int_{a}^{b}f\left(x,y\right)dy$ apply when $x$ is a function of $y$?

score 130 · Answer 1 · 2018-03-17 01:34:51

130

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Does the Leibniz rule for $\frac{\partial}{\partial x}\int_{a}^{b}f\left(x,y\right)dy$ apply when $x$ is a function of $y$?

Published on 17 Mar 2018 - 1:34

score 1.7k · Answer 2 · 2018-05-05 04:40:28

1.7k

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Leibniz rule with balls

Published on 05 May 2018 - 4:40

score 113 · Answer 3 · 2018-05-20 17:26:05

113

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Integral in terms of a parametric variable

Published on 20 May 2018 - 17:26

score 13.7k · Answer 4 · 2018-11-07 01:46:46

13.7k

Views

Definite integrals solvable using the Feynman Trick

Published on 07 Nov 2018 - 1:46

score 952 · Answer 5 · 2018-11-21 03:47:18

952

Views

Seeking methods to solve $ \int_{0}^{\frac{\pi}{2}} \ln\left|2 + \tan^2(x) \right| \:dx $

Published on 21 Nov 2018 - 3:47

score 455 · Answer 6 · 2019-06-08 19:36:34

455

Views

Derivative of a double integral over a variable circular region

Published on 08 Jun 2019 - 19:36

score 841 · Answer 7 · 2019-09-27 13:50:56

841

Views

Integrating $\int_0^\pi x^4\cos(nx)\,dx$ using the Feynman trick

Published on 27 Sep 2019 - 13:50

score 253 · Answer 8 · 2014-08-04 07:07:49

253

Views

Integral $\int_0^\infty \frac{\sin^2(x)}{x^2(x^2+1)} dx$ =?

Published on 04 Aug 2014 - 7:07

score 523 · Answer 9 · 2019-11-17 16:40:50

523

Views

Leibniz rule for partial derivative

Published on 17 Nov 2019 - 16:40

score 706 · Answer 10 · 2019-11-22 05:03:27

706

Views

Feynman Trick Demonstration for $ \int_0^1 \frac{\ln\left(1-\alpha^2x^2 \right)}{\sqrt{1-x^2}}dx $

Published on 22 Nov 2019 - 5:03

score 219 · Answer 11 · 2020-04-21 05:18:12

219

Views

Using differentiation under integral sign evaluate $\int_{0}^{\frac {\pi}{2}} \ln (\frac {a+b\sin x}{a-b\sin x}) \cdot \frac {dx}{\sin x} $

Published on 21 Apr 2020 - 5:18

score 89 · Answer 12 · 2020-05-15 20:00:47

89

Views

Is Leibniz rule applied correctly?

Published on 15 May 2020 - 20:00

score 559 · Answer 13 · 2020-05-29 08:20:39

559

Views

Use differentiation under integral sign to prove $\int_{0}^{\infty} e^{-(x^2+\frac {a^2}{x^2})b^2} dx=\frac {\sqrt {\pi}}{2b} e^{-2ab^2}$

Published on 29 May 2020 - 8:20

score 331 · Answer 14 · 2020-06-13 06:31:17

331

Views

Question about proof of Leibniz's integral rule.

Published on 13 Jun 2020 - 6:31

score 752 · Answer 15 · 2020-06-16 20:18:40

752

Views

Problem with Leibniz Rule (Differentiation under the integral sign)

Published on 16 Jun 2020 - 20:18

List Question

Does the Leibniz rule for $\frac{\partial}{\partial x}\int_{a}^{b}f\left(x,y\right)dy$ apply when $x$ is a function of $y$?

Leibniz rule with balls

Integral in terms of a parametric variable

Definite integrals solvable using the Feynman Trick

Seeking methods to solve $ \int_{0}^{\frac{\pi}{2}} \ln\left|2 + \tan^2(x) \right| \:dx $

Derivative of a double integral over a variable circular region

Integrating $\int_0^\pi x^4\cos(nx)\,dx$ using the Feynman trick

Integral $\int_0^\infty \frac{\sin^2(x)}{x^2(x^2+1)} dx$ =?

Leibniz rule for partial derivative

Feynman Trick Demonstration for $ \int_0^1 \frac{\ln\left(1-\alpha^2x^2 \right)}{\sqrt{1-x^2}}dx $

Using differentiation under integral sign evaluate $\int_{0}^{\frac {\pi}{2}} \ln (\frac {a+b\sin x}{a-b\sin x}) \cdot \frac {dx}{\sin x} $

Is Leibniz rule applied correctly?

Use differentiation under integral sign to prove $\int_{0}^{\infty} e^{-(x^2+\frac {a^2}{x^2})b^2} dx=\frac {\sqrt {\pi}}{2b} e^{-2ab^2}$

Question about proof of Leibniz's integral rule.

Problem with Leibniz Rule (Differentiation under the integral sign)

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