Question

Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.

score 342 · Answer 1 · 2026-03-25 15:52:39

342

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Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.

Published on 25 Mar 2026 - 15:52

score 77 · Answer 2 · 2026-03-30 07:39:09

77

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Verification for $\int_{-\infty}^\infty \frac{\cos(az)}{z^{2n}+1}dz$

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score 75 · Answer 3 · 2026-03-28 12:48:35

75

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Leibniz rule when range of integration is defined by inequality

Published on 28 Mar 2026 - 12:48

score 49 · Answer 4 · 2026-03-27 04:38:22

49

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Show $\int _ { 0 } ^ { \infty } \frac { x \sin x } { \left( x ^ { 2 } + 1 \right) ^ { 2 } } dx = \frac { \pi } { 4 e }$ with residue theorem

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score 323 · Answer 5 · 2019-01-13 23:24:50

323

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Prove that $F(z) = \int_a^b f(t,z) dt$ is analytic

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score 424 · Answer 6 · 2019-01-14 09:07:33

424

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Can I think of a toy contour as any closed piecewise-smooth curve which is simple?

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score 83 · Answer 7 · 2019-01-14 11:00:47

83

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Contour integral calculation 2

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score 753 · Answer 8 · 2026-03-25 12:15:06

753

Views

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67

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score 55 · Answer 10 · 2019-01-19 15:28:37

55

Views

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score 1.8k · Answer 11 · 2026-03-25 10:57:29

1.8k

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Proof without words of $\oint zdz = 0$ and $\oint dz/z = 2\pi i$

Published on 25 Mar 2026 - 10:57

score 116 · Answer 12 · 2026-03-28 12:14:28

116

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Demonstrating $\int_{\pi}^{0}{ie^{-i2\pi s \epsilon e^{i\theta}}d\theta} = i\pi \space \mathrm{sgn}(s)$

Published on 28 Mar 2026 - 12:14

score 821 · Answer 13 · 2026-03-27 12:03:18

821

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Calculate the value of $\int_0^\infty \frac{\sqrt{x}\cos(\ln(x))}{x^2+1}\,dx$

Published on 27 Mar 2026 - 12:03

score 76 · Answer 14 · 2019-01-26 22:03:29

76

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evaluate $\int_0^{\infty}\frac{x^a}{x^2+1}dx$ for $a\in(0,1)$

Published on 26 Jan 2019 - 22:03

score 106 · Answer 15 · 2026-03-27 12:02:49

106

Views

How to calculate the arc part when using Residue theorem?

Published on 27 Mar 2026 - 12:02

List Question

Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.

Verification for $\int_{-\infty}^\infty \frac{\cos(az)}{z^{2n}+1}dz$

Leibniz rule when range of integration is defined by inequality

Show $\int _ { 0 } ^ { \infty } \frac { x \sin x } { \left( x ^ { 2 } + 1 \right) ^ { 2 } } dx = \frac { \pi } { 4 e }$ with residue theorem

Prove that $F(z) = \int_a^b f(t,z) dt$ is analytic

Can I think of a toy contour as any closed piecewise-smooth curve which is simple?

Contour integral calculation 2

Visualizing Cauchy's integral theorem (and complex integration in general)

Connection between sums and integrals over closed paths and their areas

Can someone help me? I started but i have problem

Proof without words of $\oint zdz = 0$ and $\oint dz/z = 2\pi i$

Demonstrating $\int_{\pi}^{0}{ie^{-i2\pi s \epsilon e^{i\theta}}d\theta} = i\pi \space \mathrm{sgn}(s)$

Calculate the value of $\int_0^\infty \frac{\sqrt{x}\cos(\ln(x))}{x^2+1}\,dx$

evaluate $\int_0^{\infty}\frac{x^a}{x^2+1}dx$ for $a\in(0,1)$

How to calculate the arc part when using Residue theorem?

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