Question

Feynman's trick to evaluate the integral $\int\limits_{0}^{2\pi}\sin^{8}(x)dx$

score 513 · Answer 1 · 2021-05-20 09:44:05

513

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Feynman's trick to evaluate the integral $\int\limits_{0}^{2\pi}\sin^{8}(x)dx$

Published on 20 May 2021 - 9:44

score 32 · Answer 2 · 2021-06-02 15:34:18

32

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How to find the derivative of an integral whose integrand is a composition of the integral limits?

Published on 02 Jun 2021 - 15:34

score 72 · Answer 3 · 2021-06-07 13:42:20

72

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Continuity of the following integral.

Published on 07 Jun 2021 - 13:42

score 155 · Answer 4 · 2021-06-10 14:49:09

155

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$\int_0^1 e^{-x^2}dx$ a clever way to get an answer

Published on 10 Jun 2021 - 14:49

score 142 · Answer 5 · 2021-06-17 19:21:34

142

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What is the derivative of $\int_0^x \frac{f(y)}{\sqrt{x-y} }$?

Published on 17 Jun 2021 - 19:21

score 66 · Answer 6 · 2021-07-14 21:06:33

66

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Conditions for differentiating under integral sign with mixed finite and infinite limits

Published on 14 Jul 2021 - 21:06

score 165 · Answer 7 · 2021-07-18 10:14:01

165

Views

Evaluating $\int_{0}^{\infty}e^{-x^2}\:dx$, I get a wrong answer: $-\frac34\sqrt{\pi}$. Where is my mistake?

Published on 18 Jul 2021 - 10:14

score 321 · Answer 8 · 2021-07-26 03:43:59

321

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Evaluating $\frac{1}{2\pi i}\int^{a+i\infty}_{a-i\infty}\frac{x^s}{s-\beta}ds$ using Feynman integration

Published on 26 Jul 2021 - 3:43

score 158 · Answer 9 · 2021-08-05 05:25:08

158

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Why $f(x)$ cannot be obtained clearly from $\int ^{b}_{a} (f(x)-3x)\; dx=a^2-b^2$

Published on 05 Aug 2021 - 5:25

score 53 · Answer 10 · 2021-08-16 10:41:19

53

Views

Exchange Partial Derivative wrt. to a Function (Function is depedent on variable of integration)

Published on 16 Aug 2021 - 10:41

score 98 · Answer 11 · 2021-08-25 14:01:33

98

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Strong Version of Leibnitz Rule for Differentiation under the Expectation

Published on 25 Aug 2021 - 14:01

score 33 · Answer 12 · 2021-09-08 08:05:29

33

Views

Is there some rule to derive a sum of $x$, with lower and upper bounds depending on $x$?

Published on 08 Sep 2021 - 8:05

score 311 · Answer 13 · 2021-09-09 03:03:54

311

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$f\left(x\right) = \int_{1}^{x}\frac{\sin(x)\cos(y)\mathrm{d}y}{y^{2}+y+1}$, find solution of $f'\left(x\right)=0$

Published on 09 Sep 2021 - 3:03

score 49 · Answer 14 · 2021-09-23 03:14:55

49

Views

Leibniz Rule with integral that has an integral in the integrand

Published on 23 Sep 2021 - 3:14

score 73 · Answer 15 · 2021-10-09 02:08:31

73

Views

Compute derivative of $k(t)=\int^{\infty}_{-\infty} \frac{\sin{tx^2}}{1+x^4}\,\textrm dx$

Published on 09 Oct 2021 - 2:08

List Question

Feynman's trick to evaluate the integral $\int\limits_{0}^{2\pi}\sin^{8}(x)dx$

How to find the derivative of an integral whose integrand is a composition of the integral limits?

Continuity of the following integral.

$\int_0^1 e^{-x^2}dx$ a clever way to get an answer

What is the derivative of $\int_0^x \frac{f(y)}{\sqrt{x-y} }$?

Conditions for differentiating under integral sign with mixed finite and infinite limits

Evaluating $\int_{0}^{\infty}e^{-x^2}\:dx$, I get a wrong answer: $-\frac34\sqrt{\pi}$. Where is my mistake?

Evaluating $\frac{1}{2\pi i}\int^{a+i\infty}_{a-i\infty}\frac{x^s}{s-\beta}ds$ using Feynman integration

Why $f(x)$ cannot be obtained clearly from $\int ^{b}_{a} (f(x)-3x)\; dx=a^2-b^2$

Exchange Partial Derivative wrt. to a Function (Function is depedent on variable of integration)

Strong Version of Leibnitz Rule for Differentiation under the Expectation

Is there some rule to derive a sum of $x$, with lower and upper bounds depending on $x$?

$f\left(x\right) = \int_{1}^{x}\frac{\sin(x)\cos(y)\mathrm{d}y}{y^{2}+y+1}$, find solution of $f'\left(x\right)=0$

Leibniz Rule with integral that has an integral in the integrand

Compute derivative of $k(t)=\int^{\infty}_{-\infty} \frac{\sin{tx^2}}{1+x^4}\,\textrm dx$

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