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Calculus II homework help

  1. Oct 18, 2006 #1
    Calculus II homework help....

    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.
    Last edited: Oct 18, 2006
  2. jcsd
  3. Oct 19, 2006 #2


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    It should be easy to see that the limits are t= 0, t= [itex]2\pi[/itex]. 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[itex]\pi[/itex].
    Last edited: Oct 20, 2006
  4. Oct 19, 2006 #3
    Thank you.
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