Question

Assume $f \in R[a, b]$. Show that if $c \in [a, b]$ then $\int_a^c f(x)dx + \int_c^b f(x)dx = \int_a^b f(x)dx$

score 493 · Answer 1 · 2026-04-21 12:44:52

493

Views

Assume $f \in R[a, b]$. Show that if $c \in [a, b]$ then $\int_a^c f(x)dx + \int_c^b f(x)dx = \int_a^b f(x)dx$

Published on 21 Apr 2026 - 12:44

score 48 · Answer 2 · 2026-05-11 03:22:32

48

Views

Need help to understand integration notation

Published on 11 May 2026 - 3:22

score 69 · Answer 3 · 2026-05-10 19:01:41

69

Views

Integral word problem check. Is this right?

Published on 10 May 2026 - 19:01

score 103 · Answer 4 · 2026-05-10 17:01:56

103

Views

First step for $\int\frac{\operatorname{gd}\left(\log x\right)}{\sqrt{1-x^2}}dx$, where $\operatorname{gd}(x)$ denotes the Gudermannian function

Published on 10 May 2026 - 17:01

score 108 · Answer 5 · 2026-05-10 17:59:29

108

Views

Solving : $2xy \cdot u_x + u_y - u = 0$

Published on 10 May 2026 - 17:59

score 3.8k · Answer 6 · 2026-05-10 18:27:44

3.8k

Views

Find the volume of the region bounded by the coordinate planes and a cylinder

Published on 10 May 2026 - 18:27

score 73 · Answer 7 · 2026-05-11 04:17:53

73

Views

What kind of integral is this, and how do you solve it?

Published on 11 May 2026 - 4:17

score 26 · Answer 8 · 2026-05-10 23:41:53

26

Views

Showing that if $K \in L_{loc}^{\infty}(\mathbb{R}^+)$ then $|K^{\star n}| \leq M(a)^n \frac{x^{n-1}}{(n-1)!}$ where $M(a)$ is the supremum on $[0,a]$

Published on 10 May 2026 - 23:41

score 77 · Answer 9 · 2026-04-11 21:31:28

77

Views

Integral by the definition solving, like derivative

Published on 11 Apr 2026 - 21:31

score 19 · Answer 10 · 2026-04-29 20:26:16

19

Views

Finding the correct family of equations for the given equation

Published on 29 Apr 2026 - 20:26

score 235 · Answer 11 · 2026-04-10 02:15:57

235

Views

Defined integral over a closed and bounded subset of $\mathbb{R}$

Published on 10 Apr 2026 - 2:15

score 3k · Answer 12 · 2026-04-16 15:07:11

3k

Views

Find the volume of the region common to the interiors of the cylinders

Published on 16 Apr 2026 - 15:07

score 416 · Answer 13 · 2026-05-10 17:15:34

416

Views

What's the intuition behind change of variables?

Published on 10 May 2026 - 17:15

score 65 · Answer 14 · 2026-04-17 03:55:59

65

Views

show that $\int_{0}^{1}[a-(a-b)x]dx = \frac{1}{b-a}\int_{a}^{b}(x)dx$

Published on 17 Apr 2026 - 3:55

score 31 · Answer 15 · 2026-04-11 09:10:18

31

Views

How to prove the below equality?

Published on 11 Apr 2026 - 9:10

List Question

Assume $f \in R[a, b]$. Show that if $c \in [a, b]$ then $\int_a^c f(x)dx + \int_c^b f(x)dx = \int_a^b f(x)dx$

Need help to understand integration notation

Integral word problem check. Is this right?

First step for $\int\frac{\operatorname{gd}\left(\log x\right)}{\sqrt{1-x^2}}dx$, where $\operatorname{gd}(x)$ denotes the Gudermannian function

Solving : $2xy \cdot u_x + u_y - u = 0$

Find the volume of the region bounded by the coordinate planes and a cylinder

What kind of integral is this, and how do you solve it?

Showing that if $K \in L_{loc}^{\infty}(\mathbb{R}^+)$ then $|K^{\star n}| \leq M(a)^n \frac{x^{n-1}}{(n-1)!}$ where $M(a)$ is the supremum on $[0,a]$

Integral by the definition solving, like derivative

Finding the correct family of equations for the given equation

Defined integral over a closed and bounded subset of $\mathbb{R}$

Find the volume of the region common to the interiors of the cylinders

What's the intuition behind change of variables?

show that $\int_{0}^{1}[a-(a-b)x]dx = \frac{1}{b-a}\int_{a}^{b}(x)dx$

How to prove the below equality?

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