- #1
mickellowery
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Homework Statement
Consider the ellipse given by the parametric equation x=3cos(t) y=sin(t) 0[tex]\leq[/tex]t[tex]\leq[/tex]2[tex]\Pi[/tex]. Set up an integral that gives the circumference of the ellipse. Also find the area enclosed by the ellipse.
Homework Equations
[tex]\int[/tex][tex]\sqrt{1+(dy/dx)^2}[/tex]dt
The Attempt at a Solution
[tex]\int[/tex][tex]\sqrt{1+(-2/3 cot(t))^2}[/tex]dt It should also be the integral from 0 to 2[tex]\Pi[/tex] I'm not sure what I did wrong but I know that -2/3 cot(t) is not right.
area: A=2[tex]\int[/tex]1/2 (2/3 tan(t))dt
=[tex]\int2/3 tan(t)dt[/tex]
=-2/3ln(lcos(t)l) evaluated from [tex]\Pi[/tex] to 0
I know that I got something wrong here too, and I assume it is the 2/3 tan(t) but I'm not sure what I did wrong again.
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