Question

Prove $\int_0^{\infty} \frac{\cos xt}{1+t^2} dt = \frac{\pi}{2}e^{-x}$ by using Laplace Transform

score 612 · Answer 1 · 2026-04-08 22:25:37

612

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Prove $\int_0^{\infty} \frac{\cos xt}{1+t^2} dt = \frac{\pi}{2}e^{-x}$ by using Laplace Transform

Published on 08 Apr 2026 - 22:25

score 807 · Answer 2 · 2026-04-10 22:07:34

807

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Fundamental theorem of calculus with finitely many discontinuities

Published on 10 Apr 2026 - 22:07

score 242 · Answer 3 · 2026-04-02 08:08:43

242

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Evaluate: $\int \sqrt {\tan (x)} dx$

Published on 02 Apr 2026 - 8:08

score 581 · Answer 4 · 2026-03-25 09:28:16

581

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Approximating magnitude of sum of two vectors

Published on 25 Mar 2026 - 9:28

score 122 · Answer 5 · 2026-04-11 13:33:55

122

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How to rephrase these delta epsilon inequalities?

Published on 11 Apr 2026 - 13:33

score 178 · Answer 6 · 2026-04-11 15:45:41

178

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Fourier transform of PDF of t-distribution

Published on 11 Apr 2026 - 15:45

score 36 · Answer 7 · 2026-04-10 19:39:03

36

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Prove if $\lim_{k \rightarrow \infty} (c_k)^{1/k}=0$, the the radius of convergence $R=\infty$.

Published on 10 Apr 2026 - 19:39

score 118 · Answer 8 · 2026-04-08 22:27:31

118

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Prove the fact that two integrals are equal

Published on 08 Apr 2026 - 22:27

score 71 · Answer 9 · 2026-04-10 06:50:03

71

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Leibniz rule for double integral?

Published on 10 Apr 2026 - 6:50

score 767 · Answer 10 · 2026-04-08 23:40:17

767

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Why is the inverse of the derivative of f not the actual derivative of the inverse of f?

Published on 08 Apr 2026 - 23:40

score 49 · Answer 11 · 2026-04-10 05:49:41

49

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The definition of integral equations (beginner question)

Published on 10 Apr 2026 - 5:49

score 116 · Answer 12 · 2026-03-25 06:06:43

116

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About the value of the integral $\int_0^\pi\sqrt{1+t^2}\,\mathrm dt$

Published on 25 Mar 2026 - 6:06

score 216 · Answer 13 · 2026-03-24 22:07:45

216

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How to compute $\lim_{x\to 0}\frac{e^x -1-x-\frac{x^2}{2}}{x^3}$ without using L'Hospital rule?

Published on 24 Mar 2026 - 22:07

score 109 · Answer 14 · 2026-04-11 22:18:49

109

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a problem that I'm stuck on in Calculus:Integration

Published on 11 Apr 2026 - 22:18

score 86 · Answer 15 · 2026-03-25 06:06:49

86

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Showing that $g(x) = \begin{cases} f(x), & \ x \ne 0 \\ c, & \ x = 0 \end{cases}$ is Riemann integrable where $f$ is Riemann integrable

Published on 25 Mar 2026 - 6:06

List Question

Prove $\int_0^{\infty} \frac{\cos xt}{1+t^2} dt = \frac{\pi}{2}e^{-x}$ by using Laplace Transform

Fundamental theorem of calculus with finitely many discontinuities

Evaluate: $\int \sqrt {\tan (x)} dx$

Approximating magnitude of sum of two vectors

How to rephrase these delta epsilon inequalities?

Fourier transform of PDF of t-distribution

Prove if $\lim_{k \rightarrow \infty} (c_k)^{1/k}=0$, the the radius of convergence $R=\infty$.

Prove the fact that two integrals are equal

Leibniz rule for double integral?

Why is the inverse of the derivative of f not the actual derivative of the inverse of f?

The definition of integral equations (beginner question)

About the value of the integral $\int_0^\pi\sqrt{1+t^2}\,\mathrm dt$

How to compute $\lim_{x\to 0}\frac{e^x -1-x-\frac{x^2}{2}}{x^3}$ without using L'Hospital rule?

a problem that I'm stuck on in Calculus:Integration

Showing that $g(x) = \begin{cases} f(x), & \ x \ne 0 \\ c, & \ x = 0 \end{cases}$ is Riemann integrable where $f$ is Riemann integrable

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