# Math Help - Evaluate line integral (parabola)

1. ## Evaluate line integral (parabola)

Evaluate the line integral $\int^._c F \cdot dr$
where C is the portion of the parabola y = x^2 from (0,0) to (1,1) if $F(x,y) = <3ye^{xy}, 3x^2>$

This is what i get. Can anyone check this for me please thanks!

$c: r(t) = $ where 0 < t < 1

$\frac{dr}{dt} = <1,2t>$

$F(r(t)) = <3te^t^3, 3t^2>$

$F(r(t)) \cdot \frac{dr}{dt} = <3t^2e^t^3, 3t^2> \cdot <1,2t> = 3t^2e^t^3 + 6t^3$

$\int_0^1 3t^2e^t^3dt + \int_0^1 6t^3dt$

$(e-1) + \frac{3}{2} = e + \frac{1}{2}$

Thanks for looking over this

2. This is right. You just made a little mistake in the first component of F(r(t)). It has a factor of t^2 (not t). You actually corrected this later on, so your answer is correct.

Also, it should be dr/dt (not just dr).

3. Thank you. Changes were corrected in post