Question

When is it appropriate to apply a change of variable during integration?

score 1k · Answer 1 · 2026-03-25 03:01:25

1k

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When is it appropriate to apply a change of variable during integration?

Published on 25 Mar 2026 - 3:01

score 111 · Answer 2 · 2018-07-26 00:32:37

111

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$\int_9^{16} f(x)dx = 64$, what is value of $\int_9^{16} f(x^2)xdx$

Published on 26 Jul 2018 - 0:32

score 84 · Answer 3 · 2018-07-26 17:26:33

84

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When is the integral of $x^{-1} = \ln \lvert x \rvert$?

Published on 26 Jul 2018 - 17:26

score 206 · Answer 4 · 2026-03-25 00:04:25

206

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Prove that $\sqrt{1-x^2} + \sqrt{1-y^2} + \sqrt{1-z^2}\geq 4\sqrt{\frac{3-(x^2+y^2+z^2)}{5+x^2+y^2+z^2}}$.

Published on 25 Mar 2026 - 0:04

score 145 · Answer 5 · 2018-07-27 02:21:59

145

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Where did I go wrong in my working? - integration via substitution $\int_{0}^{\frac{1}{2}\ln3}\frac{1}{e^x+e^{-x}}dx$.

Published on 27 Jul 2018 - 2:21

score 175 · Answer 6 · 2018-07-29 14:18:53

175

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Given $t = \tan \frac{\theta}{2}$, show $\sin \theta = \frac{2t}{1+t^2}$

Published on 29 Jul 2018 - 14:18

score 300 · Answer 7 · 2018-07-31 12:41:28

300

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Integral of $\sqrt{4 - x^2}$?

Published on 31 Jul 2018 - 12:41

score 1.8k · Answer 8 · 2018-08-01 07:23:09

Find the number of real solutions of equation : $\sin (3\theta) = 4\sin\theta\sin(2\theta) \sin(4\theta)$ in $\theta \in (0, \pi)$.

score 168 · Answer 9 · 2018-08-02 03:49:49

168

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How to evaluate the definite integral $\int_0^{a/2 }x^2(a^2-x^2)^{-3/2}dx $

Published on 02 Aug 2018 - 3:49

score 393 · Answer 10 · 2018-08-05 02:27:18

393

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Putnam 1985 B5 Integration by Substitution

Published on 05 Aug 2018 - 2:27

score 354 · Answer 11 · 2018-08-05 06:21:38

354

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inequality involving $(xy+yz+zx)^3$ and the $pqr$ method

Published on 05 Aug 2018 - 6:21

score 356 · Answer 12 · 2026-03-25 04:35:36

356

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Inequality with $abc=2$

Published on 25 Mar 2026 - 4:35

score 504 · Answer 13 · 2018-08-06 01:01:26

504

Views

symmetric polynomial recursion to solve the system, $x^5+y^5=33$, $x+y=3$

Published on 06 Aug 2018 - 1:01

score 366 · Answer 14 · 2018-08-07 06:22:06

366

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Let $m$ be the largest real root of the equation $\frac3{x-3} + \frac5{x-5}+\frac{17}{x-17}+\frac{19}{x-19} =x^2 - 11x -4$ find $m$

Published on 07 Aug 2018 - 6:22

score 1.6k · Answer 15 · 2026-03-25 00:02:54

1.6k

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Prove that: $xy\sqrt{z}+yz\sqrt{x}+zx\sqrt{y}\geq x+y+z$

Published on 25 Mar 2026 - 0:02

List Question

When is it appropriate to apply a change of variable during integration?

$\int_9^{16} f(x)dx = 64$, what is value of $\int_9^{16} f(x^2)xdx$

When is the integral of $x^{-1} = \ln \lvert x \rvert$?

Prove that $\sqrt{1-x^2} + \sqrt{1-y^2} + \sqrt{1-z^2}\geq 4\sqrt{\frac{3-(x^2+y^2+z^2)}{5+x^2+y^2+z^2}}$.

Where did I go wrong in my working? - integration via substitution $\int_{0}^{\frac{1}{2}\ln3}\frac{1}{e^x+e^{-x}}dx$.

Given $t = \tan \frac{\theta}{2}$, show $\sin \theta = \frac{2t}{1+t^2}$

Integral of $\sqrt{4 - x^2}$?

Find the number of real solutions of equation : $\sin (3\theta) = 4\sin\theta\sin(2\theta) \sin(4\theta)$ in $\theta \in (0, \pi)$.

How to evaluate the definite integral $\int_0^{a/2 }x^2(a^2-x^2)^{-3/2}dx $

Putnam 1985 B5 Integration by Substitution

inequality involving $(xy+yz+zx)^3$ and the $pqr$ method

Inequality with $abc=2$

symmetric polynomial recursion to solve the system, $x^5+y^5=33$, $x+y=3$

Let $m$ be the largest real root of the equation $\frac3{x-3} + \frac5{x-5}+\frac{17}{x-17}+\frac{19}{x-19} =x^2 - 11x -4$ find $m$

Prove that: $xy\sqrt{z}+yz\sqrt{x}+zx\sqrt{y}\geq x+y+z$

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