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Area of a Polar Function

  1. May 14, 2010 #1
    My question here is do I have the correct limits of integration? At first I thought it would be from pi/10 to 3pi/10 but I have a feeling that those are incorrect.

    1. The problem statement, all variables and given/known data

    Find the area of one petal of the polar function r(x) = cos(5x)

    2. Relevant equations

    integral[alpa to beta] .5* r(x)^2dx

    3. The attempt at a solution

    cos(5x) = 0 when x = (1/5)*pi/2 = pi/10
    This means that the limits of integration are pi/10 and -pi/10

    integral (.5*cos(5x))dx = 1/4x - (sin(5x)/20) from pi/10 to -pi/10
  2. jcsd
  3. May 14, 2010 #2


    Staff: Mentor

    Yes, these are correct.
    You have it in your relevant equations, but you forgot to square r(x) in the integral just above. Or maybe you just forgot to put in the exponent in your integrand.
  4. May 14, 2010 #3
    Oops....sorry cos(5x)^2 = (1+cos(5x))/2

    Thanks! for some reason I was thinking it was between pi/10 and 3pi/10.
  5. May 14, 2010 #4
    That would work too. :)
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