Question

Integration by parts twice problem

score 277 · Answer 1 · 2026-04-14 05:21:11

277

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Integration by parts twice problem

Published on 14 Apr 2026 - 5:21

score 1.2k · Answer 2 · 2026-04-16 11:04:02

1.2k

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Consider the bisection method starting with the interval $[1.5, 3.5]$

Published on 16 Apr 2026 - 11:04

score 1.2k · Answer 3 · 2026-04-07 12:08:31

1.2k

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Taking the derivative of a quadratic form

Published on 07 Apr 2026 - 12:08

score 64 · Answer 4 · 2026-04-07 14:49:09

64

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Let $f:\mathbb{R}^2\to \mathbb{R}$ be of class $C^1$, with $f(2,-1)=-1$. Set $G(x,y,u)=f(x,y)+u^2, H(x,y,u)= ux+3y^3+u^3$.

Published on 07 Apr 2026 - 14:49

score 167 · Answer 5 · 2026-04-17 09:45:27

167

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Prove an integration inequality $\int_{0}^{1}\,\left(\int_{0}^{x}\,f(y)\,{\rm d}y\right)^2{\rm d}x\leqslant -\frac{mM}{6(M-m)^2}(3m^2-8mM+3M^2)$

Published on 17 Apr 2026 - 9:45

score 32 · Answer 6 · 2026-04-14 13:43:59

32

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Is $\lim\limits_{n \to \infty} f(x_{0} + \frac{1}{n}) = \lim\limits_{h \to 0^{+}} f(x_{0} + h) \triangleq f(x_{0}^{+})$?

Published on 14 Apr 2026 - 13:43

score 54 · Answer 7 · 2026-04-12 07:43:05

54

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Antiderivatives

Published on 12 Apr 2026 - 7:43

score 40 · Answer 8 · 2026-04-14 20:45:34

40

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A 2-Part Test (or The Squeeze Thm.) Question

Published on 14 Apr 2026 - 20:45

score 313 · Answer 9 · 2026-04-21 07:54:07

313

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Demonstrate that $(x+y)\ln \left(\frac{x+y}{2}\right) \leq x\ln x +y\ln y$

Published on 21 Apr 2026 - 7:54

score 5k · Answer 10 · 2026-04-16 10:53:52

5k

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Find the total distance traveled by a particle between $t = 1$ and $t = 3$

Published on 16 Apr 2026 - 10:53

score 770 · Answer 11 · 2026-04-20 07:31:14

770

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When is the Euler-Lagrange equation trivially satisfied?

Published on 20 Apr 2026 - 7:31

score 51 · Answer 12 · 2026-04-15 09:06:50

51

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If $f(x)$ is defined on $x \in (a, b)$, then where is its integral, $F(x) = \int_c^x f(t) dt$, defined (for $c \in (a, b)$)?

Published on 15 Apr 2026 - 9:06

score 6.5k · Answer 13 · 2026-04-12 02:30:51

6.5k

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How to find an antiderivative of f double prime x?

Published on 12 Apr 2026 - 2:30

score 232 · Answer 14 · 2026-04-11 18:57:30

232

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Example of a multivariable nondifferentiable function with directional derivatives.

Published on 11 Apr 2026 - 18:57

score 207 · Answer 15 · 2026-04-11 02:51:10

207

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Is there a more elegant way to solve this integral?

Published on 11 Apr 2026 - 2:51

List Question

Integration by parts twice problem

Consider the bisection method starting with the interval $[1.5, 3.5]$

Taking the derivative of a quadratic form

Let $f:\mathbb{R}^2\to \mathbb{R}$ be of class $C^1$, with $f(2,-1)=-1$. Set $G(x,y,u)=f(x,y)+u^2, H(x,y,u)= ux+3y^3+u^3$.

Prove an integration inequality $\int_{0}^{1}\,\left(\int_{0}^{x}\,f(y)\,{\rm d}y\right)^2{\rm d}x\leqslant -\frac{mM}{6(M-m)^2}(3m^2-8mM+3M^2)$

Is $\lim\limits_{n \to \infty} f(x_{0} + \frac{1}{n}) = \lim\limits_{h \to 0^{+}} f(x_{0} + h) \triangleq f(x_{0}^{+})$?

Antiderivatives

A 2-Part Test (or The Squeeze Thm.) Question

Demonstrate that $(x+y)\ln \left(\frac{x+y}{2}\right) \leq x\ln x +y\ln y$

Find the total distance traveled by a particle between $t = 1$ and $t = 3$

When is the Euler-Lagrange equation trivially satisfied?

If $f(x)$ is defined on $x \in (a, b)$, then where is its integral, $F(x) = \int_c^x f(t) dt$, defined (for $c \in (a, b)$)?

How to find an antiderivative of f double prime x?

Example of a multivariable nondifferentiable function with directional derivatives.

Is there a more elegant way to solve this integral?

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