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Homework Help: Line integral Question

  1. Jul 26, 2011 #1
    1. The problem statement, all variables and given/known data

    calculate the integral f · dr for the given vector field f(x, y) and curve C:
    f(x, y) = (x^2 + y^2) i; C : x = 2 + cos t, y = sin t, 0 ≤ t ≤ 2π (2pi)

    2. Relevant equations

    Would the vector F simply be <(x^2+y^2),0> since there is no j component?
    The solution is 4pi and I'm getting zero.

    3. The attempt at a solution
    integral of C = F · dr
    F = <((2+cos t)^2 + (sin t)^2),o> = <(5 + 4 cos t), 0>
    dr = <-sin t, cos t>

    Integral of C [0, 2pi] <(5 + 4 cos t), 0> · <-sin t, cos t> = 0 :(

    I'm thinking that my error lies in the vector I'm using for F.
  2. jcsd
  3. Jul 26, 2011 #2


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    Science Advisor

    If the problem is exactly as you stated, then the correct answer is 0.
  4. Jul 26, 2011 #3
    That's right, the F vector function only has a i component. It would be equivalent as writing it as F(x,y) = <x^2 + y^2, 0>

    BTW I posted this same exact problem. :P where did you find this?
  5. Jul 26, 2011 #4
  6. Jul 26, 2011 #5
    ^Haha. I'm self teaching myself Multivariable Calculus using this online book: http://www.mecmath.net/calc3book.pdf in conjuction with Youtube's UCBerkely Multivariable Calc lectures.

    It's just weird because I did all the steps and analyzed each step and can't see where I went wrong...we may be right because I see you got 0 too, sometimes the books make errors. I just don't see how we can get 4pi when we're evaluating an integral involving trig. when it's going to give us a rational number.
  7. Jul 27, 2011 #6
    I was doing the same with that same book. :P There were a few other errors too in other parts. I think the book just needs more revising.
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