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Evaluate Line integral

  1. Jul 29, 2008 #1
    1. The problem statement, all variables and given/known data
    Evaluate the line integral, where C is the given curve.
    integral of xy^4. C is the right half of the circle x^2 + y^2 =16

    2. Relevant equations
    integral of line integral= integral of r(t) |r'(t)| dt


    3. The attempt at a solution
    I set up a parametric equation to be r(t)=(4cost, 4sint)
    then r'(t)=(-4sint, 4cost) --> |r'(t)|=4
    My t is between -pi/2 and pi/2---these are my limits of integration.

    With the limits of integration, my integrand is (4)(cost)(sint)^4. Setting my u=sint, my final answer came out to be 8/5. I know I got the wrong answer though...
     
    Last edited: Jul 29, 2008
  2. jcsd
  3. Jul 29, 2008 #2

    nrqed

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    Why did you use pi/4 and -pi/4?? If you you plug those values in your parametrized curve, you don't get the limits corresponding to the right half of a circle! Or am I missing something?
     
  4. Jul 29, 2008 #3
    Well isn't the right half of the circle just when x>0? So I thought it would correspond to all values of y...
     
  5. Jul 29, 2008 #4

    nrqed

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    Right
    Your parametrized curve is 4 cos(t), 4 sin(t)

    If you plug t = pi/4 in that what do you get?
     
  6. Jul 29, 2008 #5
    Ah, sorry. I mean to say -pi/2 to pi/2. I just fixed it.
     
  7. Jul 29, 2008 #6

    nrqed

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    Ok. The other error is that the radius is 2, not 4. So you must changed your parametrized curve
     
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