Question

Where did the author uses, injectivity and continuous differentiability of $f$?

score 48 · Answer 1 · 2021-01-06 16:01:08

48

Views

Where did the author uses, injectivity and continuous differentiability of $f$?

Published on 06 Jan 2021 - 16:01

score 117 · Answer 2 · 2021-01-06 17:07:52

117

Views

For Riemann integral partitions, does it matter whether $f$ is evaluated at a point in $(t_{i-1},t_i)$ or $[t_{i-1},t_i]$?

Published on 06 Jan 2021 - 17:07

score 254 · Answer 3 · 2021-01-09 01:17:22

254

Views

Why are the Left and Right Riemann sums for $\int_a^b f(x)\ dx$ equal?

Published on 09 Jan 2021 - 1:17

score 108 · Answer 4 · 2026-03-29 07:21:15

108

Views

Simple question on Mean value theorem

Published on 29 Mar 2026 - 7:21

score 116 · Answer 5 · 2021-01-11 20:28:30

116

Views

Equivalent definition of Riemann integral.

Published on 11 Jan 2021 - 20:28

score 29 · Answer 6 · 2021-01-12 09:54:01

29

Views

find the measure of this set

Published on 12 Jan 2021 - 9:54

score 96 · Answer 7 · 2021-01-14 06:54:39

96

Views

$\int_0^1 f(x)dx=\lim_{n\to\infty}\frac{1}{n}\sum_{i=1}^n f(i/n)$ is not valid for non-monotone function.

Published on 14 Jan 2021 - 6:54

score 98 · Answer 8 · 2021-01-14 18:48:03

98

Views

Integral inequality related to increasing functions

Published on 14 Jan 2021 - 18:48

score 71 · Answer 9 · 2021-01-15 02:13:55

71

Views

Is $\lvert \int_0^t e^{isB_s} ds \rvert^2 \leq \left( \int_0^t \lvert e^{isB_s}\rvert ds\right)^2 = \left( \int_0^t 1 ds \right)^2 = t^2$ correct?

Published on 15 Jan 2021 - 2:13

score 315 · Answer 10 · 2021-01-15 17:17:26

315

Views

Prove that the lower Riemann integral of $f$ on $[a, b]$

Published on 15 Jan 2021 - 17:17

score 62 · Answer 11 · 2021-01-16 01:17:34

62

Views

Can one say that $\int_{r_{a}}^{r_{b}} \mathrm{d}\vec{r}$ is the infinite sum of infinitesimal magnitudes, $\mathrm{d}r$, with direction, $\hat{r}$?

Published on 16 Jan 2021 - 1:17

score 161 · Answer 12 · 2026-04-01 06:33:47

161

Views

Is it inuitively correct to say that $\lim_{n \to \infty} \frac{x}{n} = \mathrm{d}x$?

Published on 01 Apr 2026 - 6:33

score 581 · Answer 13 · 2021-01-16 09:24:25

581

Views

If $\psi=x\sin(\frac{1}{x})$, and $f$ is integrable, is then $f\circ \psi$ also integrable?

Published on 16 Jan 2021 - 9:24

score 66 · Answer 14 · 2021-01-16 14:34:46

66

Views

Show that $m\le\left(\frac{1}{b-a}\int_{a}^{b}f^{2}\left(x\right)dx\right)^{\frac{1}{2}}\le M$

Published on 16 Jan 2021 - 14:34

score 222 · Answer 15 · 2021-01-16 14:59:52

222

Views

Show that $L(f)=\sup\{L(P,f):P \in \mathcal P_{c}\}$,where $c\in \left(a,b\right)$

Published on 16 Jan 2021 - 14:59

List Question

Where did the author uses, injectivity and continuous differentiability of $f$?

For Riemann integral partitions, does it matter whether $f$ is evaluated at a point in $(t_{i-1},t_i)$ or $[t_{i-1},t_i]$?

Why are the Left and Right Riemann sums for $\int_a^b f(x)\ dx$ equal?

Simple question on Mean value theorem

Equivalent definition of Riemann integral.

find the measure of this set

$\int_0^1 f(x)dx=\lim_{n\to\infty}\frac{1}{n}\sum_{i=1}^n f(i/n)$ is not valid for non-monotone function.

Integral inequality related to increasing functions

Is $\lvert \int_0^t e^{isB_s} ds \rvert^2 \leq \left( \int_0^t \lvert e^{isB_s}\rvert ds\right)^2 = \left( \int_0^t 1 ds \right)^2 = t^2$ correct?

Prove that the lower Riemann integral of $f$ on $[a, b]$

Can one say that $\int_{r_{a}}^{r_{b}} \mathrm{d}\vec{r}$ is the infinite sum of infinitesimal magnitudes, $\mathrm{d}r$, with direction, $\hat{r}$?

Is it inuitively correct to say that $\lim_{n \to \infty} \frac{x}{n} = \mathrm{d}x$?

If $\psi=x\sin(\frac{1}{x})$, and $f$ is integrable, is then $f\circ \psi$ also integrable?

Show that $m\le\left(\frac{1}{b-a}\int_{a}^{b}f^{2}\left(x\right)dx\right)^{\frac{1}{2}}\le M$

Show that $L(f)=\sup\{L(P,f):P \in \mathcal P_{c}\}$,where $c\in \left(a,b\right)$

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