Results 1 to 8 of 8

Math Help - Find length of polar curve

  1. #1
    CML
    CML is offline
    Newbie
    Joined
    Mar 2010
    Posts
    3

    Find length of polar curve

    How do I find the length of the polar curve
    r = 4sin(3theta)
    I know what the formula for the length of a polar curve is, but the answer I get seems to be too small.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2010
    Posts
    993
    Thanks
    244
    You should have the basic formula:

    s=\int_{\theta_1}^{\theta_2}\sqrt{r^2+\left(\frac{  dr}{d\theta}\right)^2}d\theta

    The curve has six lobes, so your answer should be greater than 6 times (4 out and 4 in) = 48. And it should be less than 6 times the perimeter of an equilateral triangle with height 4, or 6 times 3 times 8/sqrt(3) = 48sqrt(3).

    If you show me your attempt at the problem I can probably help more. Post in this thread and I'll try to answer as soon as possible.

    - Hollywood
    Follow Math Help Forum on Facebook and Google+

  3. #3
    CML
    CML is offline
    Newbie
    Joined
    Mar 2010
    Posts
    3
    Sorry, I'm new here, so I'm not sure how to put my reply in equations, but what I did was:
    Integral from 0 to pi of [16sin^2(3theta) + 144cos^2(3theta)]^(1/2)

    I'm not even sure if the end points for the integral are right. The more I try it the more lost I get
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Mar 2010
    Posts
    993
    Thanks
    244
    I made a mistake in my last post - the graph has 3 lobes, not 6. So the length should be between 24 and 24sqrt(3). Sorry about that.

    I think your setup is correct. I thought the integral would be easy, but I can't seem to get it. Does anyone know how to integrate this function?

    \int_{0}^{\pi}\sqrt{16sin^23x+144cos^23x}\ dx
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Mar 2010
    Posts
    993
    Thanks
    244
    For what it's worth, I was able to get a numerical value: 26.73.

    - Hollywood
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Mar 2010
    Posts
    993
    Thanks
    244
    I can pull some constants out of the integral:

    \frac{4}{3}\int_{0}^{3\pi}\sqrt{sin^2u+9cos^2u}\ du

    I've tried changing the integrand to \sqrt{1+8\cos^2u} and \sqrt{5+4cos{2u}}, but that doesn't seem to make it any easier.

    - Hollywood
    Follow Math Help Forum on Facebook and Google+

  7. #7
    CML
    CML is offline
    Newbie
    Joined
    Mar 2010
    Posts
    3
    In response to your PM I got it from my calc text book: Stewart essential Calculus. I too got the numerical answer, but I'm sure it must be able to be done by hand. But it was for an assignment, and I've already handed it in, so it's not a huge deal anymore. Thanks for your help
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    Joined
    Mar 2010
    Posts
    993
    Thanks
    244
    Ok. Let us know if you get the solution.

    - Hollywood
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Polar length of curve
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 6th 2010, 07:24 AM
  2. length of polar curve
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 19th 2010, 03:18 PM
  3. length of polar curve
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 23rd 2009, 12:27 AM
  4. Find the length of the spiraling polar curve
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 15th 2009, 10:44 AM
  5. Length of a Polar Curve
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 16th 2008, 10:26 PM

Search Tags


/mathhelpforum @mathhelpforum