Finding the Length of an Astroid Curve in Calculus II

[sristi]

Calculus II homework help...

Hi,
I am new to this forum and I found about this forum on talk.collegeconfidential.com. Well I have been having some trouble with my Calc II work . It would be great if someone could explain this problem to be

Find the total length of the astroid x=a (cos t)^3, y=a (sin t)^3, where a>0.

I think I know how to find the equation for the integral but I don't know how to find the limits.

Here is the work that I did so far:

x'=-3a cos^2 sin
y'= 3a sin^2 cos

I set those equal to zero to find the critical points. I got 0, pi/2, pi, 3pi/2, 2pi. Then I got stuck. I tried graphing it in the parametric mode in my calculator but I got a weird looking graph...

Any help would be appreciated. Thanks.

 

[HallsofIvy]

It should be easy to see that the limits are t= 0, t= 2\pi. You graph should be a diamond with sides "bulging" inward. Because the graph is in all four quadrants, each of x, y must be both positive and negative and you only get that for sine and cosine with the variable going from 0 to 2\pi.

 

[sristi]

Thank you.