Question

Show that there exists an $\alpha \in (0,1)$ such that $\int_{0}^{\pi} x^{\alpha}\sin x dx=3$

score 157 · Answer 1 · 2026-04-15 06:12:53

157

Views

Show that there exists an $\alpha \in (0,1)$ such that $\int_{0}^{\pi} x^{\alpha}\sin x dx=3$

Published on 15 Apr 2026 - 6:12

score 152 · Answer 2 · 2026-04-15 06:38:09

152

Views

Is there any way to evaluate $\int_0^\infty \cos(bx) \sinh(\pi x) \left[ K_{ix}(a) \right]^2 \, dx?$

Published on 15 Apr 2026 - 6:38

score 403 · Answer 3 · 2026-04-15 20:17:52

403

Views

Area of fourth quadrant in unit circle

Published on 15 Apr 2026 - 20:17

score 171 · Answer 4 · 2026-04-13 09:40:08

171

Views

integral of arccos

Published on 13 Apr 2026 - 9:40

score 258 · Answer 5 · 2026-04-10 03:59:27

258

Views

Substitution in complex integration

Published on 10 Apr 2026 - 3:59

score 206 · Answer 6 · 2026-04-16 13:21:44

206

Views

Compute $\int_0^1\frac {\sqrt{x}}{(x+3)\sqrt{x+3}}dx.$

Published on 16 Apr 2026 - 13:21

score 280 · Answer 7 · 2026-04-17 15:05:35

280

Views

Evaluating $\int_0^1\frac{\ln^2(1+x^2)}{x^4}dx$

Published on 17 Apr 2026 - 15:05

score 40 · Answer 8 · 2026-04-13 15:08:57

40

Views

What does evaluating a definite integral where the limits are functions represent?

Published on 13 Apr 2026 - 15:08

score 69 · Answer 9 · 2026-04-12 00:45:07

69

Views

Integration on Maple

Published on 12 Apr 2026 - 0:45

score 46 · Answer 10 · 2026-04-15 13:38:31

46

Views

Integral over set given by $x^2+y^2 \le 1, \frac {1}{\sqrt{3}} \le \frac{y}{x} \le \sqrt 3, z \le 1$

Published on 15 Apr 2026 - 13:38

score 36 · Answer 11 · 2026-04-08 17:31:50

36

Views

Estimating an integral in terms of a parameter

Published on 08 Apr 2026 - 17:31

score 658 · Answer 12 · 2026-04-09 11:44:11

658

Views

How to evaluate this Riemann integral using this definition?

Published on 09 Apr 2026 - 11:44

score 336 · Answer 13 · 2026-04-12 07:42:14

336

Views

When $\Big[ uv \Big]_{x\,:=\,0}^{x\,:=\,1}$ and $\int_{x\,:=\,0}^{x\,:=\,1} v\,du$ are infinite but $\int_{x\,:=\,0}^{x\,:=\,1}u\,dv$ is finite

Published on 12 Apr 2026 - 7:42

score 97 · Answer 14 · 2026-04-10 21:01:37

97

Views

Problem on Definite Integration

Published on 10 Apr 2026 - 21:01

score 61 · Answer 15 · 2026-04-14 09:15:41

61

Views

Estimation of some Integrals, which exceeded Wolfram Alpha's free computation time.

Published on 14 Apr 2026 - 9:15

List Question

Show that there exists an $\alpha \in (0,1)$ such that $\int_{0}^{\pi} x^{\alpha}\sin x dx=3$

Is there any way to evaluate $\int_0^\infty \cos(bx) \sinh(\pi x) \left[ K_{ix}(a) \right]^2 \, dx?$

Area of fourth quadrant in unit circle

integral of arccos

Substitution in complex integration

Compute $\int_0^1\frac {\sqrt{x}}{(x+3)\sqrt{x+3}}dx.$

Evaluating $\int_0^1\frac{\ln^2(1+x^2)}{x^4}dx$

What does evaluating a definite integral where the limits are functions represent?

Integration on Maple

Integral over set given by $x^2+y^2 \le 1, \frac {1}{\sqrt{3}} \le \frac{y}{x} \le \sqrt 3, z \le 1$

Estimating an integral in terms of a parameter

How to evaluate this Riemann integral using this definition?

When $\Big[ uv \Big]_{x\,:=\,0}^{x\,:=\,1}$ and $\int_{x\,:=\,0}^{x\,:=\,1} v\,du$ are infinite but $\int_{x\,:=\,0}^{x\,:=\,1}u\,dv$ is finite

Problem on Definite Integration

Estimation of some Integrals, which exceeded Wolfram Alpha's free computation time.

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