Question

If F(x)=$\int_0^xf(x)dx$ for $x\in[0,3]$, find $F$. Find $F'(x)$ at all points where $F'$ exists.

score 60 · Answer 1 · 2026-04-15 22:24:39

60

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If F(x)=$\int_0^xf(x)dx$ for $x\in[0,3]$, find $F$. Find $F'(x)$ at all points where $F'$ exists.

Published on 15 Apr 2026 - 22:24

score 52 · Answer 2 · 2026-04-16 06:18:15

52

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Using FTC, find $F'(x)$ where $F$ is defined on $[0,\infty)$ by $F(x)=\int_x^{e^x}\sqrt{1+t^2}dt.$

Published on 16 Apr 2026 - 6:18

score 26 · Answer 3 · 2026-05-10 17:18:08

26

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What's the meaning of h(T) in this Darboux sums theorem?

Published on 10 May 2026 - 17:18

score 82 · Answer 4 · 2026-04-16 11:05:37

82

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Is it always possible to choose $x \in (a, b)$ s.t. $\int_a^{x}f=\int_x^{b}f$

Published on 16 Apr 2026 - 11:05

score 1.3k · Answer 5 · 2026-04-09 09:13:58

1.3k

Views

Difference between a Riemann integral and an integral against a measure

Published on 09 Apr 2026 - 9:13

score 67 · Answer 6 · 2026-04-09 08:35:27

67

Views

Another definition of Riemann Integral

Published on 09 Apr 2026 - 8:35

score 1.6k · Answer 7 · 2026-04-14 11:24:47

1.6k

Views

Why can Lebesgue integral be defined only with supremum, but Riemanns needs both sup. and inf.?

Published on 14 Apr 2026 - 11:24

score 827 · Answer 8 · 2026-04-15 12:05:11

827

Views

Show that $g$ is Riemann integrable on $I$

Published on 15 Apr 2026 - 12:05

score 1.3k · Answer 9 · 2026-04-14 18:35:09

1.3k

Views

Rudin Theorem 6.10 doubt

Published on 14 Apr 2026 - 18:35

score 167 · Answer 10 · 2026-04-14 21:53:03

167

Views

convergence of improper integral wrt comparison to improper integrals known to exist

Published on 14 Apr 2026 - 21:53

score 4.4k · Answer 11 · 2026-04-09 21:53:05

4.4k

Views

Composition of Riemann integrable and continuous function is integrable

Published on 09 Apr 2026 - 21:53

score 2.5k · Answer 12 · 2026-04-14 02:54:59

2.5k

Views

Why is the integral defined as the limit of the sum $\int_a^b f(x) dx = \lim_{n\to\infty}\sum_{i=1}^n f(x_i^*)\Delta x$?

Published on 14 Apr 2026 - 2:54

score 107 · Answer 13 · 2026-04-13 07:35:44

107

Views

How can I solve this sequence with Riemann integration?

Published on 13 Apr 2026 - 7:35

score 1.3k · Answer 14 · 2026-04-16 03:09:11

1.3k

Views

How can I evaluate $\lim_{n \rightarrow \infty} \int_n^\infty \frac{n^2 \arctan {\frac{1}{x}}}{x^2+n^2}\ dx$?

Published on 16 Apr 2026 - 3:09

score 66 · Answer 15 · 2026-04-15 10:19:08

66

Views

Continous Function on [a, b] $\implies$ Riemann Integrable without use of uniform continuity

Published on 15 Apr 2026 - 10:19

List Question

If F(x)=$\int_0^xf(x)dx$ for $x\in[0,3]$, find $F$. Find $F'(x)$ at all points where $F'$ exists.

Using FTC, find $F'(x)$ where $F$ is defined on $[0,\infty)$ by $F(x)=\int_x^{e^x}\sqrt{1+t^2}dt.$

What's the meaning of h(T) in this Darboux sums theorem?

Is it always possible to choose $x \in (a, b)$ s.t. $\int_a^{x}f=\int_x^{b}f$

Difference between a Riemann integral and an integral against a measure

Another definition of Riemann Integral

Why can Lebesgue integral be defined only with supremum, but Riemanns needs both sup. and inf.?

Show that $g$ is Riemann integrable on $I$

Rudin Theorem 6.10 doubt

convergence of improper integral wrt comparison to improper integrals known to exist

Composition of Riemann integrable and continuous function is integrable

Why is the integral defined as the limit of the sum $\int_a^b f(x) dx = \lim_{n\to\infty}\sum_{i=1}^n f(x_i^*)\Delta x$?

How can I solve this sequence with Riemann integration?

How can I evaluate $\lim_{n \rightarrow \infty} \int_n^\infty \frac{n^2 \arctan {\frac{1}{x}}}{x^2+n^2}\ dx$?

Continous Function on [a, b] $\implies$ Riemann Integrable without use of uniform continuity

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