# 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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### Using Gauss theorem to evaluate the flux

Given $$F(x,y,z)=(x^3+\sin(z),x^2y+\cos(z),\exp(x^2+y^2))$$ I have to evaluate the flux of $F$ through $S$, with $S$ being the surface of $Q$, such that $Q$ is bounded by the cylinder $$z=4-x^2$$ the ...
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### Calculation of Surface Integration.

I've been studying surface integration by myself, but I'm always stuck at the last step. Consider the above question: This is my approach: Calculation of the curl of the given field. Calculation of ...
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### Change of variables method for surface integrals

Let $\phi: \partial B_1(0) \to \mathbb{R}$ be a differentiable function where $\partial B_1(0) = \{x \in \mathbb{R}^n : |x| = 1\}$ . Defining: $$S = \{\phi(x)x : x\in \partial B_1(0)\}$$ I am ...
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### How to solve these complicated SA and arc length integrals?

My partner and I are working on a project for our multivariable calculus class where we have to solve the integrals to find the arc length and surface area of our three piecewise functions. We've used ...
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### How to prove an object $\in R^3$ with its surface area finite must also have its volume finite?
Suppose that $f(x)>0$ is a continuously differentiable function defined on $x\ge 1$. Let $S$ be the surface of revolution of the graph $y=f(x)$ about $x-axis$. Let $E \subset R^3$ be the solid ...
Calculate the area of the surface Y given by the equation $z = x^2 + y^2 − 1$ when $z ≤ 0$ Here is my solution: I got the answer correct but there is something I just did (not toally randomly but I ...