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differentiating a 2 dimensional line integral

Posted 10 years ago

I am relatively new to mathematica and I need for a course to calculate the following derivative.

$\dfrac{\partial \int_{L(\alpha,u)} f(x,y,t) d(x,y)}{\partial t}$ with $L(\alpha,u) = \{ (x,y) | x cos(\alpha) + y sin(\alpha) = u \}$ for $\alpha \in [0,\pi[$ and $u \in \mathbb{R}$ for a certain function $f(x,y,t)$.

The problem is that I don't know how to set the condition $x cos(\alpha) + y sin(\alpha) = u$ in an integral.

Can someone help me with this?

Thanks in advance

Koen

POSTED BY: koen ruymbeek

This syntax may give what you want:

With[{f = Function[{x, y, t}, t/(1 + x^2 + y^2)], \[Alpha] = Pi/4, 
  u = 1},
 Integrate[f[x, y, t], 
  Element[{x, y}, 
   ImplicitRegion[x*Cos[\[Alpha]] + y*Sin[\[Alpha]] == u, {x, y}]]]]
POSTED BY: Gianluca Gorni
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