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Math Help - Tricky Line Integral

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    Tricky Line Integral

    integral P of (x + y)dx + dy, where P is given by g(t) = (t,t^2), 0 <= t <= 1.
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  2. #2
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    \displaystyle x = t \implies dx = dt, y = t^2 \implies dy = 2t\,dt.

    Therefore

    \displaystyle \int_P{[(x + y)\,dx + dy]} = \int_0^1{[(t + t^2)\,dt + 2t\,dt]}

    \displaystyle = \int_0^1{(3t + t^2)\,dt}.

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