Question

Show that integration is a linear operator

score 11.5k · Answer 1 · 2017-07-25 09:33:22

11.5k

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Show that integration is a linear operator

Published on 25 Jul 2017 - 9:33

score 56 · Answer 2 · 2026-04-03 09:14:51

56

Views

Show that if $f: [a, b] \to \Bbb{R}$ is Riemann integrable, then $\int_a^xf(s)ds$ is uniformly continuous on $[a, b]$

Published on 03 Apr 2026 - 9:14

score 836 · Answer 3 · 2026-03-31 10:17:19

836

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Prove the Riemann integral $\int_{a}^{b} x^2 dx = \frac{b^3-a^3}{3}$ by using the mean value theorem

Published on 31 Mar 2026 - 10:17

score 1.9k · Answer 4 · 2026-03-31 10:07:34

1.9k

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Evaluate Riemann integral $\int_{a}^{b} e^x dx$ using upper and lower integral definitions and theorems

Published on 31 Mar 2026 - 10:07

score 98 · Answer 5 · 2017-07-28 17:58:17

98

Views

Showing $f(x)$ is continuous.

Published on 28 Jul 2017 - 17:58

score 134 · Answer 6 · 2017-07-29 13:21:43

134

Views

Prove that the value of integral is 0

Published on 29 Jul 2017 - 13:21

score 179 · Answer 7 · 2026-03-31 10:13:42

179

Views

Applying $ \cos(j-1) \theta - \cos(j+1)\theta = 2\sin\theta \sin j \theta$ to find the Riemann integral $\int_0^b \sin x \, dx$

Published on 31 Mar 2026 - 10:13

score 188 · Answer 8 · 2017-07-30 05:46:45

188

Views

Using Riemann definitions, Prove that $\int_{a}^{b} (c_1f_1+...c_nf_n) = c_1 \int_a^b f_1(x) dx + ...+ c_n\int_a^b f_n(x) dx$

Published on 30 Jul 2017 - 5:46

score 8.5k · Answer 9 · 2026-03-31 10:17:16

8.5k

Views

Prove that If $f$ is integrable on $[a,b]$ and $[b,c]$ then $f$ is integrable on $[a,c]$

Published on 31 Mar 2026 - 10:17

score 201 · Answer 10 · 2026-03-31 10:06:51

201

Views

$f(x)>0\implies\int_a^bf(x)\mathop{dx}>0$

Published on 31 Mar 2026 - 10:06

score 3.4k · Answer 11 · 2017-08-01 12:38:45

3.4k

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Show that $f(x) = 2x+3$ is Riemann integrable on interval [2,3]

Published on 01 Aug 2017 - 12:38

score 152 · Answer 12 · 2017-08-01 17:22:48

152

Views

Let $f:[a,b]\times[c,d]\rightarrow\mathbb{R}$ be continuous. Prove continuity of the function $F$

Published on 01 Aug 2017 - 17:22

score 266 · Answer 13 · 2026-02-25 15:23:27

266

Views

The greatest value of Riemann sum and integral of a function on the interval [0,10]

Published on 25 Feb 2026 - 15:23

score 85 · Answer 14 · 2017-08-03 21:21:56

85

Views

Prove that $F'(x)=f(x)$, for almost all $x\in[0,1]$.

Published on 03 Aug 2017 - 21:21

score 35 · Answer 15 · 2026-03-31 12:13:38

35

Views

How to show $x_i<x_{i-1}+\delta$?

Published on 31 Mar 2026 - 12:13

List Question

Show that integration is a linear operator

Show that if $f: [a, b] \to \Bbb{R}$ is Riemann integrable, then $\int_a^xf(s)ds$ is uniformly continuous on $[a, b]$

Prove the Riemann integral $\int_{a}^{b} x^2 dx = \frac{b^3-a^3}{3}$ by using the mean value theorem

Evaluate Riemann integral $\int_{a}^{b} e^x dx$ using upper and lower integral definitions and theorems

Showing $f(x)$ is continuous.

Prove that the value of integral is 0

Applying $ \cos(j-1) \theta - \cos(j+1)\theta = 2\sin\theta \sin j \theta$ to find the Riemann integral $\int_0^b \sin x \, dx$

Using Riemann definitions, Prove that $\int_{a}^{b} (c_1f_1+...c_nf_n) = c_1 \int_a^b f_1(x) dx + ...+ c_n\int_a^b f_n(x) dx$

Prove that If $f$ is integrable on $[a,b]$ and $[b,c]$ then $f$ is integrable on $[a,c]$

$f(x)>0\implies\int_a^bf(x)\mathop{dx}>0$

Show that $f(x) = 2x+3$ is Riemann integrable on interval [2,3]

Let $f:[a,b]\times[c,d]\rightarrow\mathbb{R}$ be continuous. Prove continuity of the function $F$

The greatest value of Riemann sum and integral of a function on the interval [0,10]

Prove that $F'(x)=f(x)$, for almost all $x\in[0,1]$.

How to show $x_i<x_{i-1}+\delta$?

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