# Questions tagged [surface-integrals]

In mathematics, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analog of the line integral.

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### Calculating a surface integral of a surface by another surface

Let $\Sigma$ be the surface $\frac{x^2}{2}+y^2=1$, $0\leq z\leq 1$ and $u(x,y,z)=\frac{x}{x^2+y^2},\frac{y}{x^2+y^2},z^2-z)$. Calculate the flux integral $\iint_\Sigma (u|N)dS$ where $N$ points away ...
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### Calculating Electric Flux Through a Closed Surface

I'm trying to solve a problem involving the calculation of electric flux through a closed surface, but it's my first time attempting such a problem and I could use some guidance. Any help would be ...
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### The surface integral $\iint_S (z^2 + y^2 + x^2) \, dS$ over the cube $S$? [closed]

Evaluate the integral $$\iint_S (z^2 + y^2 + x^2) \, dS ,$$ where $S$ is the surface of the cube $\{-a < x < a, -a < y< a, -a< z< a\}$. I've attempted to partition the surface into ...
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### How to solve this kind of surface integral with Hamilton Operator?

In $\mathbb{R}^3$, $f=\left(\frac{x}{2}\right)^2+\left(\frac{y}{2}\right)^2+\left(\frac{z}{4}\right)^2$, Surface $S$ is defined by $S=\{(x,y,z)|f(x,y,z)=1, z>0\}$, and the vector field $A$ is ...
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### How to calculate the limits of the integral and the outward vector? How to make change of variables in this proof?

I would like to see the calculations behind this proof I found here: Proof of polar coordinates theorem in Evans' PDE Book That is, I am struggling to understand the following: How do we ...
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