- #1
randomcat
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Homework Statement
Evaluate ∫ F ds over the curve C for:
a) F = (x, -y) and r(t) = (cos t, sin t), 0 ≤ t ≤ 2∏
b) F = (yz, xz, xy) where the curve C consists of straight-line segments joining (1, 0, 0) to (0, 1, 0) to (0, 0, 1)
Homework Equations
The Attempt at a Solution
a) I first found the norm:
r'(t) = (-sin t, cos t)
||r'(t)|| = 1
Now my question is, how do I set up the integral? I know that F = (cos t, -sin t), and I have found the norm, but I'm lost about how toI go about setting up the integral.
b) Let C1 be the vector from (1, 0, 0) to (0, 1, 0) and let C2 be the vector from (0, 1, 0) to (0, 0, 1)
I parametrize C1: r(t) = (1-t, t, 0)
C2: r(t) = (0, 1-t, t)
Again, I can find the norm easily once I have the parametrization, but how do I set up the integral?