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Question regarding substitution in integral

score 45 · Answer 1 · 2026-03-25 06:00:04

45

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Question regarding substitution in integral

Published on 25 Mar 2026 - 6:00

score 65 · Answer 2 · 2026-03-25 21:48:00

65

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finding roots of an equation

Published on 25 Mar 2026 - 21:48

score 408 · Answer 3 · 2026-03-26 07:52:43

408

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Let $x, y, z$ be real numbers. If $x + y + z = 1$ and $x^2 + y^2 + z^2 = 1$, then what is the minimum value of $x^3 + y^3 + z^3$?

Published on 26 Mar 2026 - 7:52

score 361 · Answer 4 · 2019-07-14 08:55:35

361

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Integral clarification

Published on 14 Jul 2019 - 8:55

score 141 · Answer 5 · 2026-03-25 07:46:30

141

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Given three positive numbers $x,y,z$ so that $x+y+z=\frac{3}{2}$. Prove that $28\,x^2y^2z^2+3(x^2y^2+y^2z^2+z^2x^2)\leqq1$ .

Published on 25 Mar 2026 - 7:46

score 150 · Answer 6 · 2026-03-25 09:28:30

150

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Prove $x+y+z \ge xy+yz+zx$

Published on 25 Mar 2026 - 9:28

score 273 · Answer 7 · 2026-03-25 06:13:03

273

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Given three positive numbers $a,b,c$. Prove that $\sum\limits_{cyc}\sqrt{\frac{a+b}{b+1}}\geqq3\sqrt[3]{\frac{4\,abc}{3\,abc+1}}$ .

Published on 25 Mar 2026 - 6:13

score 231 · Answer 8 · 2019-07-15 18:50:00

231

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Can we cancel out $1$ after replacing $e^x$ in $e^x-1$ by its Taylor expansion when calculating a limit?

Published on 15 Jul 2019 - 18:50

score 617 · Answer 9 · 2026-03-25 14:22:55

617

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Integral of product of error function and Gaussian

Published on 25 Mar 2026 - 14:22

score 292 · Answer 10 · 2019-07-16 19:34:58

292

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Compute the integral $\int\limits_0^1 \frac{3x}{\sqrt{4-3x^2}} dx $?

Published on 16 Jul 2019 - 19:34

score 90 · Answer 11 · 2026-03-25 11:03:45

90

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Given positive $a, b, c$, prove that $(a^2 + b^2 + c^2)^3 \ge (a^3 + b^3 + c^3)(ab + bc + ca)(a + b + c)$.

Published on 25 Mar 2026 - 11:03

score 53 · Answer 12 · 2019-07-18 17:15:09

53

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How to find $u$ for $u$ substitution in $\frac{1}{x^2+4}$

Published on 18 Jul 2019 - 17:15

score 65 · Answer 13 · 2019-07-19 23:43:11

65

Views

Using hyperbolic substitution, wrong coefficient

Published on 19 Jul 2019 - 23:43

score 470 · Answer 14 · 2019-07-20 00:51:01

470

Views

Why are the extremes of integration considered values of $x$ when computing an integral by substitution?

Published on 20 Jul 2019 - 0:51

score 91 · Answer 15 · 2019-07-24 10:20:12

91

Views

Given a, b, c are positive number, $abc=a+b+c$ prove $ab+4bc+9ac≥36$

Published on 24 Jul 2019 - 10:20

List Question

Question regarding substitution in integral

finding roots of an equation

Let $x, y, z$ be real numbers. If $x + y + z = 1$ and $x^2 + y^2 + z^2 = 1$, then what is the minimum value of $x^3 + y^3 + z^3$?

Integral clarification

Given three positive numbers $x,y,z$ so that $x+y+z=\frac{3}{2}$. Prove that $28\,x^2y^2z^2+3(x^2y^2+y^2z^2+z^2x^2)\leqq1$ .

Prove $x+y+z \ge xy+yz+zx$

Given three positive numbers $a,b,c$. Prove that $\sum\limits_{cyc}\sqrt{\frac{a+b}{b+1}}\geqq3\sqrt[3]{\frac{4\,abc}{3\,abc+1}}$ .

Can we cancel out $1$ after replacing $e^x$ in $e^x-1$ by its Taylor expansion when calculating a limit?

Integral of product of error function and Gaussian

Compute the integral $\int\limits_0^1 \frac{3x}{\sqrt{4-3x^2}} dx $?

Given positive $a, b, c$, prove that $(a^2 + b^2 + c^2)^3 \ge (a^3 + b^3 + c^3)(ab + bc + ca)(a + b + c)$.

How to find $u$ for $u$ substitution in $\frac{1}{x^2+4}$

Using hyperbolic substitution, wrong coefficient

Why are the extremes of integration considered values of $x$ when computing an integral by substitution?

Given a, b, c are positive number, $abc=a+b+c$ prove $ab+4bc+9ac≥36$

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