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

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.

2. Relevant equations

[tex]\int[/tex][tex]\sqrt{1+(dy/dx)^2}[/tex]dt

3. 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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# Equation of the circumference of an ellipse parametric equations

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