Question

Evaluate the improper integral ${\int_0^{ + \infty } {\frac{{\cos t^2 - \sin t^2 }}{{1 + t^4 }}} dt}.$

score 208 · Answer 1 · 2026-04-17 20:42:45

208

Views

Evaluate the improper integral ${\int_0^{ + \infty } {\frac{{\cos t^2 - \sin t^2 }}{{1 + t^4 }}} dt}.$

Published on 17 Apr 2026 - 20:42

score 354 · Answer 2 · 2026-04-13 14:55:50

354

Views

What is $\lim_{x\to\infty}\frac{\int_{0}^{x}\cos\{t-\cos t\}dt}{x}$?

Published on 13 Apr 2026 - 14:55

score 165 · Answer 3 · 2026-04-16 21:00:23

165

Views

Find $\lim _{n \rightarrow+\infty} n \sqrt{n} \int_0^{+\infty} \frac{\sin x^2}{\left(1+x^2\right)^n} d x$

Published on 16 Apr 2026 - 21:00

score 257 · Answer 4 · 2026-04-10 16:24:28

257

Views

Is there a convergent improper integral for an unbounded function?

Published on 10 Apr 2026 - 16:24

score 272 · Answer 5 · 2026-04-12 05:40:50

272

Views

Can we evaluate the Fresnel integral of a quadratic in general using real methods?

Published on 12 Apr 2026 - 5:40

score 50 · Answer 6 · 2026-04-14 08:13:11

50

Views

What is the correct way for splitting this improper integral?

Published on 14 Apr 2026 - 8:13

score 161 · Answer 7 · 2026-04-16 04:12:52

161

Views

How to evaluate $ \displaystyle \int_0^\infty \frac {\sin x}{1+x^3}dx. $?

Published on 16 Apr 2026 - 4:12

score 53 · Answer 8 · 2026-04-15 16:44:21

53

Views

Convergence of $\int_0^1 \int_0^1 (1-xy)^{-a}dxdy$

Published on 15 Apr 2026 - 16:44

score 51 · Answer 9 · 2026-04-13 19:54:32

51

Views

Are negative powers of cosine Lebesgue-integrable?

Published on 13 Apr 2026 - 19:54

score 131 · Answer 10 · 2026-04-16 03:20:43

131

Views

How to tackle this integral $\int_0^1 \frac{x^p}{1-x} \ln \frac{1}{x} dx\quad (p>-1)$

Published on 16 Apr 2026 - 3:20

score 209 · Answer 11 · 2026-04-17 06:06:46

209

Views

Calculate $\int_0^\infty \frac{\sin\left(x^2 - \arctan\left(\frac{1}{x^2}\right)\right)}{\sqrt{1 + x^4}} \, dx $

Published on 17 Apr 2026 - 6:06

score 53 · Answer 12 · 2026-04-14 14:34:13

53

Views

Integral of product of Bessel functions of different order

Published on 14 Apr 2026 - 14:34

score 342 · Answer 13 · 2026-04-16 07:15:07

342

Views

How to integrate $I = \int_{0}^{\infty} \frac{e^{-x}\sin^4(x)}{x^{2}}\,dx$

Published on 16 Apr 2026 - 7:15

score 145 · Answer 14 · 2026-04-14 03:26:49

145

Views

Showing that an upper sum is an upper bound of the improper integral

Published on 14 Apr 2026 - 3:26

score 551 · Answer 15 · 2026-04-11 18:55:02

551

Views

What does this sequence of integral converge to?

Published on 11 Apr 2026 - 18:55

List Question

Evaluate the improper integral ${\int_0^{ + \infty } {\frac{{\cos t^2 - \sin t^2 }}{{1 + t^4 }}} dt}.$

What is $\lim_{x\to\infty}\frac{\int_{0}^{x}\cos\{t-\cos t\}dt}{x}$?

Find $\lim _{n \rightarrow+\infty} n \sqrt{n} \int_0^{+\infty} \frac{\sin x^2}{\left(1+x^2\right)^n} d x$

Is there a convergent improper integral for an unbounded function?

Can we evaluate the Fresnel integral of a quadratic in general using real methods?

What is the correct way for splitting this improper integral?

How to evaluate $ \displaystyle \int_0^\infty \frac {\sin x}{1+x^3}dx. $?

Convergence of $\int_0^1 \int_0^1 (1-xy)^{-a}dxdy$

Are negative powers of cosine Lebesgue-integrable?

How to tackle this integral $\int_0^1 \frac{x^p}{1-x} \ln \frac{1}{x} dx\quad (p>-1)$

Calculate $\int_0^\infty \frac{\sin\left(x^2 - \arctan\left(\frac{1}{x^2}\right)\right)}{\sqrt{1 + x^4}} \, dx $

Integral of product of Bessel functions of different order

How to integrate $I = \int_{0}^{\infty} \frac{e^{-x}\sin^4(x)}{x^{2}}\,dx$

Showing that an upper sum is an upper bound of the improper integral

What does this sequence of integral converge to?

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