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

Find the length of the ellipse [tex]9x^2 + 10y^2 = 90[/tex] correct to six decimal places.

2. Relevant equations

[tex]4L[/tex]arc in the first quadrant = [tex]L[/tex]ellipse

3. The attempt at a solution

Just checking to see if I did this right:

[tex]9x^2 + 10y^2 = 90[/tex]

[tex]x^2/10 + y^2/9 = 1[/tex]

Therefore a = [tex]\sqrt{10}[/tex] and b = 3.

This makes [tex]x = \sqrt{10}sin t[/tex] and [tex]y = 3 cos t[/tex]

Since [tex]\int \sqrt{(dx)^2 + (dy)^2}[/tex] is the formula for arc length, do I just get: [tex]4\int \sqrt{10(cos t)^2 - 9(sin t)^2}[/tex]?

And are the bounds just from 0 to [tex]\pi/2[/tex]?

Thanks!

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# Length of the ellipse

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