# Thread: Tricky Line Integral

1. ## Tricky Line Integral

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

2. $\displaystyle x = t \implies dx = dt, y = t^2 \implies dy = 2t\,dt$.

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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