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Math Help - A vector equation thingy

  1. #1
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    A vector equation thingy

    Calculate \int_{C}f(X).dX where f(x,y)=(x^2+xy,y-x^2y) and C is parametrized by x=t, y= \frac{1}{t} \; (1\leq t \leq 3)

    I'm not really sure how to go about this. This is what I've attempted:
    x=t \Rightarrow \tfrac{\delta x}{\delta t} = 1
    y= \tfrac{1}{t} \Rightarrow \tfrac{\delta y}{\delta t} = -\tfrac{1}{t^2}

    \int_{C}f(X).dX = \int_{C} (x^2+xy).\partial x + (y-x^2y).\partial y = \int_{1}^{3} (t^2+1-\frac{1}{t^3}+\frac{1}{t}).\partial t

    integrating that makes for a unpleasant mess: \frac{t^3}{3}+t+\frac{1}{2t^2}+ln(t) which is why I'm wondering if I'm doing this right.
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  2. #2
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    Believe it or not, that is exactly right!
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  3. #3
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    Also try
    \int_{C}f(X(t))\cdot X'(t) dt
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