Question

Prove/disprove that if $f$ is cont, decreasing on $[1, \infty)$, and $\lim_{x \to \infty} f(x) = 0$, then $\int^{\infty}_{1}f(x)dx$ converges.

score 143 · Answer 1 · 2017-02-16 02:51:28

143

Views

Prove/disprove that if $f$ is cont, decreasing on $[1, \infty)$, and $\lim_{x \to \infty} f(x) = 0$, then $\int^{\infty}_{1}f(x)dx$ converges.

Published on 16 Feb 2017 - 2:51

score 679 · Answer 2 · 2017-02-16 11:27:06

679

Views

How can I evaluate the following integral? $\int(\sqrt{x}-x)(e^{\arctan\sqrt{x}})^2dx$

Published on 16 Feb 2017 - 11:27

score 358 · Answer 3 · 2017-02-16 14:11:22

358

Views

Change of variables to get the Gaussian Integral

Published on 16 Feb 2017 - 14:11

score 327 · Answer 4 · 2017-02-16 19:00:31

327

Views

Proving multivariable result for evaluating odd functions

Published on 16 Feb 2017 - 19:00

score 48 · Answer 5 · 2017-02-17 10:22:24

48

Views

Solving an indefinite integral

Published on 17 Feb 2017 - 10:22

score 38 · Answer 6 · 2026-04-04 15:12:35

38

Views

Minimizing Integral

Published on 04 Apr 2026 - 15:12

score 3k · Answer 7 · 2017-02-17 16:07:17

3k

Views

The 'd' symbol in integration and derivation

Published on 17 Feb 2017 - 16:07

score 14.3k · Answer 8 · 2017-02-17 19:36:39

14.3k

Views

Integral $\int\frac{(1 - x)^2 e^x}{(1 + x^2)^2}dx$

Published on 17 Feb 2017 - 19:36

score 108 · Answer 9 · 2026-04-01 21:33:38

108

Views

How can we find a closed form solution of $\int(x+a)^m(x+b)^n~dx$?

Published on 01 Apr 2026 - 21:33

score 72 · Answer 10 · 2017-02-19 17:04:32

72

Views

Indefinite integration of $\frac{\exp(x)}{\sqrt(x)}$

Published on 19 Feb 2017 - 17:04

score 1.2k · Answer 11 · 2026-04-01 00:26:37

1.2k

Views

Can you use the substitution $t=\tan(x/2)$ to solve $\int \frac{1}{\cos x}dx$?

Published on 01 Apr 2026 - 0:26

score 407 · Answer 12 · 2017-02-20 20:57:44

407

Views

confusion about why areas of integrals below y=0 are always negative

Published on 20 Feb 2017 - 20:57

score 273 · Answer 13 · 2017-02-21 09:05:53

273

Views

How to take the integral? $\int \frac{x^2-3x+2}{x^2+2x+1}dx$

Published on 21 Feb 2017 - 9:05

score 87 · Answer 14 · 2026-03-29 07:39:25

87

Views

How to take the integral $\;\int\frac{\sin^2x\,dx}{\cos^4x}$

Published on 29 Mar 2026 - 7:39

score 157 · Answer 15 · 2017-02-21 11:37:55

157

Views

How to take the integral $\int\frac{dx}{\sin^3x}$

Published on 21 Feb 2017 - 11:37

List Question

Prove/disprove that if $f$ is cont, decreasing on $[1, \infty)$, and $\lim_{x \to \infty} f(x) = 0$, then $\int^{\infty}_{1}f(x)dx$ converges.

How can I evaluate the following integral? $\int(\sqrt{x}-x)(e^{\arctan\sqrt{x}})^2dx$

Change of variables to get the Gaussian Integral

Proving multivariable result for evaluating odd functions

Solving an indefinite integral

Minimizing Integral

The 'd' symbol in integration and derivation

Integral $\int\frac{(1 - x)^2 e^x}{(1 + x^2)^2}dx$

How can we find a closed form solution of $\int(x+a)^m(x+b)^n~dx$?

Indefinite integration of $\frac{\exp(x)}{\sqrt(x)}$

Can you use the substitution $t=\tan(x/2)$ to solve $\int \frac{1}{\cos x}dx$?

confusion about why areas of integrals below y=0 are always negative

How to take the integral? $\int \frac{x^2-3x+2}{x^2+2x+1}dx$

How to take the integral $\;\int\frac{\sin^2x\,dx}{\cos^4x}$

How to take the integral $\int\frac{dx}{\sin^3x}$

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