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Mean value of $r$ with respect to $\theta$ between two limits of a polar curve

score 1k · Answer 1 · 2026-05-14 17:13:38

1k

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Mean value of $r$ with respect to $\theta$ between two limits of a polar curve

Published on 14 May 2026 - 17:13

score 60 · Answer 2 · 2026-04-14 17:23:09

60

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Is $F(x)=\int _{\sqrt x}^{1}\arcsin(t^2) \,dt$ differentiable?

Published on 14 Apr 2026 - 17:23

score 131 · Answer 3 · 2026-04-15 19:09:27

131

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computing $\int_{-\infty}^{\infty}\frac{x^3\sin(ax)}{x^4+b^4}$

Published on 15 Apr 2026 - 19:09

score 67 · Answer 4 · 2026-04-17 09:49:29

67

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Evaluate $\int_{0}^{\infty}\frac{\ln^m(x)}{\prod_{k=0}^{n}(1+\alpha_k x)}\mathrm dx=G(m)$

Published on 17 Apr 2026 - 9:49

score 201 · Answer 5 · 2026-05-10 21:58:33

201

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If $f'(a):\mathbb R^m\to \mathbb R^m$ is not an isomorphism, then

Published on 10 May 2026 - 21:58

score 2.6k · Answer 6 · 2026-05-14 19:40:28

2.6k

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Proof that integral of uniformly convergent series converges to sum of the integrals

Published on 14 May 2026 - 19:40

score 133 · Answer 7 · 2026-05-05 09:13:54

133

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Find the following limit: $ \lim_{n \to \infty} \frac{1}{n} \int_0^\infty e^{-x/n}f(x) \, dx. $

Published on 05 May 2026 - 9:13

score 47 · Answer 8 · 2026-04-23 02:09:51

47

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Find $\int_D {e^{f(x, y)} \left(g(x, y)\right)^2 \text{d}x \, \text{d}y}$

Published on 23 Apr 2026 - 2:09

score 1.2k · Answer 9 · 2026-05-10 19:15:50

1.2k

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triple integral- plane/cone

Published on 10 May 2026 - 19:15

score 151 · Answer 10 · 2026-04-11 20:58:25

151

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monotonic function is riemann-integrable?

Published on 11 Apr 2026 - 20:58

score 239 · Answer 11 · 2026-04-14 23:19:29

239

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Integral $\int_0^{\infty}\frac{1}{(1+x^2)(3-\cos x)}dx$

Published on 14 Apr 2026 - 23:19

score 317 · Answer 12 · 2026-04-15 17:11:18

317

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Calculate $\int_{1}^{-1} |z-1|^2 dz$ along the upper half of the circle $|z|=1$

Published on 15 Apr 2026 - 17:11

score 208 · Answer 13 · 2026-04-17 11:48:11

208

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Compute $\int_0^2\frac {\arctan{x}}{x^2+2x+2}dx$

Published on 17 Apr 2026 - 11:48

score 168 · Answer 14 · 2026-04-15 04:49:41

168

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Let $f,g$ be Riemann integrable on $[a,b]$.

Published on 15 Apr 2026 - 4:49

score 39 · Answer 15 · 2026-04-21 10:50:27

39

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Definite integral: putting value before integration

Published on 21 Apr 2026 - 10:50

List Question

Mean value of $r$ with respect to $\theta$ between two limits of a polar curve

Is $F(x)=\int _{\sqrt x}^{1}\arcsin(t^2) \,dt$ differentiable?

computing $\int_{-\infty}^{\infty}\frac{x^3\sin(ax)}{x^4+b^4}$

Evaluate $\int_{0}^{\infty}\frac{\ln^m(x)}{\prod_{k=0}^{n}(1+\alpha_k x)}\mathrm dx=G(m)$

If $f'(a):\mathbb R^m\to \mathbb R^m$ is not an isomorphism, then

Proof that integral of uniformly convergent series converges to sum of the integrals

Find the following limit: $ \lim_{n \to \infty} \frac{1}{n} \int_0^\infty e^{-x/n}f(x) \, dx. $

Find $\int_D {e^{f(x, y)} \left(g(x, y)\right)^2 \text{d}x \, \text{d}y}$

triple integral- plane/cone

monotonic function is riemann-integrable?

Integral $\int_0^{\infty}\frac{1}{(1+x^2)(3-\cos x)}dx$

Calculate $\int_{1}^{-1} |z-1|^2 dz$ along the upper half of the circle $|z|=1$

Compute $\int_0^2\frac {\arctan{x}}{x^2+2x+2}dx$

Let $f,g$ be Riemann integrable on $[a,b]$.

Definite integral: putting value before integration

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