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Homework Help: Path Integrals- Multivariable Calculus

  1. May 18, 2013 #1
    Path Integrals-- Multivariable Calculus

    Hi all-- really stuck here, help would be greatly appreciated. :)
    1. Evaluate ∫Fds (over c), where F(x, y, z) = (y, 2x, y) and the path c is de fined by the equation c(t) = (t, t^2, t^3); on [0, 1]:

    2. Relevant equations
    L = sqrt(f'(t)^2 + g'(t)^2 + h'(t)^2)dt from a to b

    3. The attempt at a solution
    I thought that F(x,y,z) could be rewritten as (t^2, 2t, t^2), F'(x,y,z) is (2t, 2, 2t)
    Then ∫Fds should be ∫√(2(2t)^2 +2^2)dt from 0 to 1.
    I don't think this is correct, though, since whenever we have integrals of the type ∫√(x^2+c)dx, our TA sends emails telling us it's okay to use Wolfram Alpha.
    Can anyone give me a hint in the right direction?
  2. jcsd
  3. May 18, 2013 #2


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    Science Advisor
    Homework Helper
    Gold Member

    You appear to be mixing scalars and vectors. You have F as a vector and ds as a scalar. One would expect either a line integral of the type ##\int\vec F\cdot d\vec R## or ##\int F(x,y,z)ds##. Which is it?
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