- #1
bigplanet401
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Homework Statement
Use the parametric equations of an ellipse, x = f(t)= a cos t and y = g(t) = b sin t, 0 <= t <= 2 pi, to find the area that it encloses.
Homework Equations
Integral for parametric equations.
The Attempt at a Solution
[tex]
A = \int_0^{2 \pi} g(t) f^\prime(t) \; dt
= \int_0^{2 \pi} -ab sin^2 t \; dt
= \frac{-ab}{2} \int_0^{2 \pi} (1 - cos 2t) \; dt
= \frac{-ab}{2} (t - \frac{1}{2} sin 2t ) \vert_0^{2 \pi}
= -\pi a b
[/tex]
But why the negative sign??