# 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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### Volume of a 3D tube

What's the way to compute the volume and the lateral area of a 3D tube with non-uniform section which axis is a spacial line L ? And what's the mathematical name of this geometry in the first place ? ...
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### surface integrals & differential forms

A 2-dimenional surface integral of a vector filed in ${\mathbb R}^3$ is given by $$\int F.dS := \int_\Omega (F\circ \phi) . (\phi_x \wedge \phi_y) d(x,y)$$ if $\phi$ is a parametrization. We can ...
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### Compute this integral (multivar. calc.)

So i have the following question: Compute $$\int_{C}(x^2+y)dx + (z+x)dy + (x+2y)dz$$ where $C$ is the intersection of the cylinder $x^2+y^2=4$ and the plane $x+y=z$ So my thoughts are to ...
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### How would one approximate the surface area of a curved shape as on these ETFE pillows?

I need to get the surface area of these ETFE pillows:
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Suppose $f\in C^1(\mathbb{R}^3)$, for every $t\in \mathbb{R}$, $f^{-1}(t)$ is a simple(1) closed surface, and let the volume of the 3-D object surrounded by $f^{-1}(t)$ be $F(t)$. If $F:[0,+\infty] \... 1answer 59 views ### Computing surface integral for$F(x,y,z) = (xy,-x^2,x+z)$Let$F: \mathbb{R}^3 \to \mathbb{R}^3, F(x,y,z) = (xy,-x^2,x+z)$be a vector field. Compute the surface integral over the set$S$which is bounded by the plane$2x+2y+z=6$in the set$\{(x,y,z) \in \...
Suppose I have two 3d surfaces $f(x, y, z) =0$and $g(x, y, z)=0$ Now further assume that if we eliminate one variable say $z$ from the above equations and find $h(y, z) =0$ Then what does this ...