Question

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

score 516 · Answer 1 · 2026-03-22 04:09:06

516

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

Published on 22 Mar 2026 - 4:09

score 35 · Answer 2 · 2026-03-22 02:18:12

35

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

Published on 22 Mar 2026 - 2:18

score 75 · Answer 3 · 2026-03-21 21:59:35

75

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Continuity of the following integral.

Published on 21 Mar 2026 - 21:59

score 158 · Answer 4 · 2026-03-22 12:12:41

158

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

Published on 22 Mar 2026 - 12:12

score 145 · Answer 5 · 2026-03-21 19:43:18

145

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

Published on 21 Mar 2026 - 19:43

score 67 · Answer 6 · 2026-02-24 09:53:08

67

Views

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

Published on 24 Feb 2026 - 9:53

score 166 · Answer 7 · 2026-02-24 09:52:04

166

Views

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

Published on 24 Feb 2026 - 9:52

score 322 · Answer 8 · 2026-02-24 09:53:06

322

Views

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

Published on 24 Feb 2026 - 9:53

score 159 · Answer 9 · 2026-02-24 09:53:25

159

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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 24 Feb 2026 - 9:53

score 54 · Answer 10 · 2026-02-24 09:49:53

54

Views

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

Published on 24 Feb 2026 - 9:49

score 99 · Answer 11 · 2026-02-24 09:51:55

99

Views

Strong Version of Leibnitz Rule for Differentiation under the Expectation

Published on 24 Feb 2026 - 9:51

score 34 · Answer 12 · 2026-02-24 09:54:58

34

Views

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

Published on 24 Feb 2026 - 9:54

score 312 · Answer 13 · 2026-02-24 09:54:22

312

Views

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

Published on 24 Feb 2026 - 9:54

score 50 · Answer 14 · 2026-02-24 09:52:16

50

Views

Leibniz Rule with integral that has an integral in the integrand

Published on 24 Feb 2026 - 9:52

score 74 · Answer 15 · 2026-02-24 09:54:02

74

Views

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

Published on 24 Feb 2026 - 9:54

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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