## Line integral under surface defined by meshgrid values – Python

I need to calculate the line integral between two points (x1,y1) and (x2,y2) under a surface defined by values on a meshgrid. I’m not exactly sure on the best tool/approach to use for this process …

## Schwarz inequality for multiple integrals: \$left[int_A f(x)g(x) dxright]^2 le int_A f(x)^2 dx cdot int_A g(x)^2 dx\$

If \$f,g:Ato mathbb{R}\$ are integrable, prove the Schwarz inequality \$\$left[int_A f(x)g(x) dxright]^2 le int_A f(x)^2 dx cdot int_A g(x)^2 dx\$\$ This is that type of question that …

## Substitution rule in complex analysis

Let \$lambda_{mathbb{C}}\$ be the Lebesgue measure in the complex plane. Let \$f\$ be an entire function and \$g\$ a continuous function. I ask: When does the substitution rule hold \$\$int_{mathbb{C}}…

## Prove that \$underline{int_A}{f(x) dx} + underline{int_A}{g(x) dx} le underline{int_A}{[f(x) + g(x)] dx}\$

Question: Let \$f,g:Atomathbb{R}\$ bounded in the set \$A\$. Prove that a) \$\$underline{int_A}{f(x) dx} + underline{int_A}{g(x) dx} le underline{int_A}{[f(x) + g(x)] dx}\le …

## Use partial Integration to show \$int_0^{frac{pi}{2}} (4x-pi)cdot cos(x) = pi – 4cdot(sqrt2-1)\$

My attempt (formula for partial integration: \$int fg = Fg – int Fg’\$): \$F(x) = sin(x), f(x) = cos(x), g(x) = 4x- pi, g'(x) = 4\$ \$sin(x)(4x-pi)- int sin(x)cdot 4 = sin(x)(4x-pi)+ 4cos(x)+…

## Using spherical coordinates to bound \$int_{mathbb{R}^n} |x-y|_2 ^{-a}dy\$?

Is it possible to bound \$\$int_{mathbb{R}^n} |x-y|_2 ^{-a}dy\$\$ with \$\$int_{mathbb{R}^n}frac{r^{n-1}}{r^a}dr\$\$ by using spherical coordinates? For \$n=3\$ this is clear, but what about \$n>3\$?