Question

Prove that $\frac{ \partial F (x)}{ \partial x_1 } = f(x) $, where $F(x) = \int_{I_{a,x}} f(t) dt$

score 30 · Answer 1 · 2026-03-24 22:51:53

30

Views

Prove that $\frac{ \partial F (x)}{ \partial x_1 } = f(x) $, where $F(x) = \int_{I_{a,x}} f(t) dt$

Published on 24 Mar 2026 - 22:51

score 385 · Answer 2 · 2026-03-25 07:16:34

385

Views

How to prove that the limit of an upper sum equals the integral of a function with these limited definitions?

Published on 25 Mar 2026 - 7:16

score 395 · Answer 3 · 2026-03-17 20:48:41

395

Views

Infinite Riemann integral implies infinite lower Riemann sum?

Published on 17 Mar 2026 - 20:48

score 118 · Answer 4 · 2026-03-25 03:04:15

118

Views

How to prove that $\int_0^1 dx \int_0^x f(x,y) dy = \int_0^1 dy \int_y^1 f(x,y) dx$ for a continuous function $f$ the given interval

Published on 25 Mar 2026 - 3:04

score 239 · Answer 5 · 2018-02-08 12:55:29

239

Views

If $f(x)$ is differentiable and $f'(x)$ is bounded, the $f(x)$ is integrable.

Published on 08 Feb 2018 - 12:55

score 317 · Answer 6 · 2018-02-13 01:35:30

317

Views

Let $f_n(x)$ be a sequence of integrable functions such that $\lim_{n\to \infty} \int^a_b |f_n(x)|dx=0$. Prove the following

Published on 13 Feb 2018 - 1:35

score 122 · Answer 7 · 2026-03-22 10:32:05

122

Views

Show that $(S_t - M_t) \phi(S_t) = \Phi(S_t) - \int_{0}^{t} \phi(S_s) dM_s$

Published on 22 Mar 2026 - 10:32

score 112 · Answer 8 · 2018-02-18 15:33:10

112

Views

What did I do wrong in this Riemann sum?

Published on 18 Feb 2018 - 15:33

score 482 · Answer 9 · 2018-02-21 10:19:40

482

Views

Moment of inertia using double integration.

Published on 21 Feb 2018 - 10:19

score 196 · Answer 10 · 2018-02-22 22:41:10

196

Views

Show that the Riemann Stieljes integral of fd$\gamma$ exists

Published on 22 Feb 2018 - 22:41

score 165 · Answer 11 · 2018-02-23 02:30:04

165

Views

Having difficulty in evaluating limit of the product

Published on 23 Feb 2018 - 2:30

score 18 · Answer 12 · 2018-02-24 14:06:11

18

Views

Composition of two differentiable functions and a related integration and its sign

Published on 24 Feb 2018 - 14:06

score 846 · Answer 13 · 2026-03-25 05:00:03

846

Views

Using Fubini's theorem for Riemann integrals

Published on 25 Mar 2026 - 5:00

score 1.4k · Answer 14 · 2018-02-25 04:47:42

1.4k

Views

Why do we use supremum instead of maximum in Riemann Integration?

Published on 25 Feb 2018 - 4:47

score 907 · Answer 15 · 2018-02-25 17:06:49

907

Views

Limit as a definite Integral

Published on 25 Feb 2018 - 17:06

List Question

Prove that $\frac{ \partial F (x)}{ \partial x_1 } = f(x) $, where $F(x) = \int_{I_{a,x}} f(t) dt$

How to prove that the limit of an upper sum equals the integral of a function with these limited definitions?

Infinite Riemann integral implies infinite lower Riemann sum?

How to prove that $\int_0^1 dx \int_0^x f(x,y) dy = \int_0^1 dy \int_y^1 f(x,y) dx$ for a continuous function $f$ the given interval

If $f(x)$ is differentiable and $f'(x)$ is bounded, the $f(x)$ is integrable.

Let $f_n(x)$ be a sequence of integrable functions such that $\lim_{n\to \infty} \int^a_b |f_n(x)|dx=0$. Prove the following

Show that $(S_t - M_t) \phi(S_t) = \Phi(S_t) - \int_{0}^{t} \phi(S_s) dM_s$

What did I do wrong in this Riemann sum?

Moment of inertia using double integration.

Show that the Riemann Stieljes integral of fd$\gamma$ exists

Having difficulty in evaluating limit of the product

Composition of two differentiable functions and a related integration and its sign

Using Fubini's theorem for Riemann integrals

Why do we use supremum instead of maximum in Riemann Integration?

Limit as a definite Integral

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