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physics_197
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Homework Statement
Consider the ellipse r(t) = <acost, bsint>, for t between 0 and 2PI, where a and b are real numbers. Let Θ be the angle between the position vector and the x-axis.
a) Recall that the area bounded by the polar curve r = f(Θ) on the interval [0,Θ] is A(Θ) = (1/2) ∫ (f(u))^2 du, where in this case f(theta) = |r(Θ(t))|. Use this fact to show that A'(t) = (1/2)ab.