Any help with the following problem would be greatly appreciated.

Set up, but do not evaluate, an integral for the length of the curve.

x^2/a^2 + y^2/b^2 = 1

Thanks.

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- Apr 4th 2010, 10:17 PMvlodgeIntegral for the length of a curve.
Any help with the following problem would be greatly appreciated.

Set up, but do not evaluate, an integral for the length of the curve.

x^2/a^2 + y^2/b^2 = 1

Thanks. - Apr 4th 2010, 11:47 PMsimplependulum
There are many methods , the choice depends on what you know about it .

we have

or parametric form :

Make as the subject , we have

and

Therefore ,

But indicates the length of the semi-ellipse but not the whole ellipse , for the whole ellipse you need to multiply by . - Apr 5th 2010, 05:55 AMHallsofIvy
As simplependulum said, you can also do this with parametric equations.

Standard parametric equations for the ellipse are x= a cos(t) and y= b sin(t). Then x'= -a sin(t) and y'= b cos(t) so the arclength is

By the way, the reason the problem said "Set up, but do not evaluate" the integral is that "ellipitic integrals" [b]cannot[b] be integrated analytically.