(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the area swept out by the line from the origin to the ellipse x=acos(t) y=asin(t) as t varies from 0 to [itex]t_{0}[/itex] where [itex]t_{0}[/itex] is a constant between 0 and 2[itex]\pi[/itex]

2. Relevant equations

3. The attempt at a solution

so using Greens Theorem in reverse i get A=[itex]\frac{1}{2}\oint_{c} ydx-xdy[/itex]

x=acos(t) dx=-asin(t)

y=asin(t) dy=cos(t)

so sub into my equation i get [itex]\frac{1}{2}\int^{t_0}_{0} a(sin^2 (t) - cos^2(t)) dt[/itex]

[itex]-\frac{1}{2}\int^{t_0}_{0} a(1) dt[/itex]

I think im good up to here, i then integrate and get [itex]-\frac{1}{2} at_0[/itex] but im not sure about how to use the information that [itex]t_0[/itex] varies from 0 to 2[itex]\pi[/itex]

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# Homework Help: Greens Theorem Area of ellipse

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