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.
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 .
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.