Question

Finding example for $ G\left(x\right)=\intop_{a}^{x}g\left(t\right)dt $ that is differntiable but $ G'\neq g $

score 55 · Answer 1 · 2020-08-16 14:47:43

55

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Finding example for $ G\left(x\right)=\intop_{a}^{x}g\left(t\right)dt $ that is differntiable but $ G'\neq g $

Published on 16 Aug 2020 - 14:47

score 277 · Answer 2 · 2020-08-16 22:31:36

277

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Step in proof on Riemann Sums from Spivak Calculus.

Published on 16 Aug 2020 - 22:31

score 181 · Answer 3 · 2026-03-31 22:47:54

181

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Suppose $f:[0,1]\to\Bbb R$ is a continuous function and $\int_0^xf=\int_x^1f$ for all $x\in[0,1]$. Show that $f(x)=0$ for every $x\in[0,1]$.

Published on 31 Mar 2026 - 22:47

score 433 · Answer 4 · 2020-08-18 17:33:12

433

Views

Prove that the following function is Riemann Integrable

Published on 18 Aug 2020 - 17:33

score 87 · Answer 5 · 2026-03-31 22:49:24

87

Views

How would I go about calculating $\int_{0}^{b}x^{3}$ using the Riemann Sum?

Published on 31 Mar 2026 - 22:49

score 159 · Answer 6 · 2020-08-19 09:15:18

159

Views

Deriving the value of $\int\limits_{-\infty}^\infty \frac{\sin(x)}{x} dx$ by way of Fourier transformation

Published on 19 Aug 2020 - 9:15

score 67 · Answer 7 · 2020-08-19 19:11:31

67

Views

Determine if a function is integrable.

Published on 19 Aug 2020 - 19:11

score 304 · Answer 8 · 2026-02-25 10:13:35

304

Views

Are Riemann integrable functions the pointwise limit of continuous functions?

Published on 25 Feb 2026 - 10:13

score 216 · Answer 9 · 2020-08-21 19:36:51

216

Views

Riemann integrability on $[-1,1]$

Published on 21 Aug 2020 - 19:36

score 135 · Answer 10 · 2020-08-22 14:05:42

135

Views

How to calculate $ \intop_{0}^{\frac{\pi}{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx $

Published on 22 Aug 2020 - 14:05

score 106 · Answer 11 · 2020-08-23 09:45:13

106

Views

Calculation of $ \int\frac{dx}{a\sin x+b\cos x} $

Published on 23 Aug 2020 - 9:45

score 100 · Answer 12 · 2026-03-26 04:53:49

100

Views

Is it true that $ \int_{\mathbb R} f(t)g(t) \, dt = \int_{\mathbb R} f'(t) \, dg(t) $?

Published on 26 Mar 2026 - 4:53

score 279 · Answer 13 · 2020-08-24 15:04:38

279

Views

Riemann integral and Cauchy integral

Published on 24 Aug 2020 - 15:04

score 183 · Answer 14 · 2020-08-24 20:43:25

183

Views

Replacing improper integral by sum of integrals

Published on 24 Aug 2020 - 20:43

score 126 · Answer 15 · 2020-08-25 20:25:18

126

Views

Let $f,g\in\mathscr{R}[a,b]$ and $f,g\geq0$ such that $\left\{\int_{a}^{b}f(x)^pdx\right\}^{\frac{1}{p}}=0$. Prove that $\int_{a}^{b}f(x)g(x)dx=0$

Published on 25 Aug 2020 - 20:25

List Question

Finding example for $ G\left(x\right)=\intop_{a}^{x}g\left(t\right)dt $ that is differntiable but $ G'\neq g $

Step in proof on Riemann Sums from Spivak Calculus.

Suppose $f:[0,1]\to\Bbb R$ is a continuous function and $\int_0^xf=\int_x^1f$ for all $x\in[0,1]$. Show that $f(x)=0$ for every $x\in[0,1]$.

Prove that the following function is Riemann Integrable

How would I go about calculating $\int_{0}^{b}x^{3}$ using the Riemann Sum?

Deriving the value of $\int\limits_{-\infty}^\infty \frac{\sin(x)}{x} dx$ by way of Fourier transformation

Determine if a function is integrable.

Are Riemann integrable functions the pointwise limit of continuous functions?

Riemann integrability on $[-1,1]$

How to calculate $ \intop_{0}^{\frac{\pi}{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx $

Calculation of $ \int\frac{dx}{a\sin x+b\cos x} $

Is it true that $ \int_{\mathbb R} f(t)g(t) \, dt = \int_{\mathbb R} f'(t) \, dg(t) $?

Riemann integral and Cauchy integral

Replacing improper integral by sum of integrals

Let $f,g\in\mathscr{R}[a,b]$ and $f,g\geq0$ such that $\left\{\int_{a}^{b}f(x)^pdx\right\}^{\frac{1}{p}}=0$. Prove that $\int_{a}^{b}f(x)g(x)dx=0$

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