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Help using Green's Theorem?
I read up on it, but I can't seem to understand how it's used. Here's a problem that requires the use of Green's theorem, if it helps make it easier, I know this is kind of advanced stuff:
using Green's theorem, calculate the surface of the curve given by:
F(t) = a cos^3(t), b cos^3(t)
for a>0, 0<_t<_2pi
1 Antwort
- No MythologyLv 7vor 8 Jahren
There is no surface enclosed by that vector valued function. You can compute the length of the curve, but it doesn't require anything fancy because it is a straight line segment traversed twice.
The curve F(t) = <a cos^3(t), b cos^3(t)> for 0 ≤ t ≤ 2π is the straight line connecting the points (a, b) and (-a, -b). As a particle path, it would start at (a, b), pass through the origin to the point (-a, -b), turn around and travel back along the line to (a, b) when t = 2π. It's length is 4√(a² + b²).
Are you sure you typed F correctly?
