# Questions tagged [line-integrals]

In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear integral are also used.

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### Find wrapping angle of helix on a torus

I need some help in calculating the wrapping angle of a spiral helix wrapped on a torus with constant angle against all the meridians of the torus. The wrapping angle (or the angle measured around and/...
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### Complex substitution allowed but changes result

It is well known that $$I := \int_L \frac{1}{z} ~\text{d}z = 2 \pi i$$ where $L$ is the complex unit circle, parametrized by $\gamma(t) = e^{it}, 0 \leq t \leq 2 \pi$. However, using complex ...
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### Using Green's Theorem to Calculate the Counter-Clockwise Circulation for the Field $\mathbf{F}$ and Curve $C$.

I have this problem Use Green’s Theorem to find the counter-clockwise circulation for the field $\mathbf{F}$ and curve $C$. with this image Green's Theorem says that the counter-clockwise ...
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### Compute the following line integral along a path of your choice (Finding potential)

Consider the following vector field: $$\vec A(x,y,z)=(yz)\hat i+(xz)\hat j+(xy)\hat k$$ Compute the line integral of $A$ along a path of your choice connecting $(0,0,0)$ to $(1,1,1).$ I recognise ...
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### Integral of 1-form $\omega=\dfrac{-y \,dx + x \,dy}{x^2 +y^2}$ over a triangle. [duplicate]

I'm trying to evaluate the integral of the $1$-form $$\omega=\dfrac{-y \,dx +x\,dy}{x^2 +y^2}$$ through the corners of a triangle with the vertices $A= (-5,-2)$, $B=(5,-2)$, $C=(0,3)$. I've ...