- #1
wilcofan3
- 27
- 0
Homework Statement
Find the length of the ellipse [tex]9x^2 + 10y^2 = 90[/tex] correct to six decimal places.
Homework Equations
[tex]4L[/tex]arc in the first quadrant = [tex]L[/tex]ellipse
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!