# Evaluate line integral (parabola)

• Dec 4th 2010, 06:21 PM
mybrohshi5
Evaluate line integral (parabola)
Evaluate the line integral $\displaystyle \int^._c F \cdot dr$
where C is the portion of the parabola y = x^2 from (0,0) to (1,1) if $\displaystyle F(x,y) = <3ye^{xy}, 3x^2>$

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

$\displaystyle c: r(t) = <t,t^2>$ where 0 < t < 1

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

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

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

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

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

Thanks for looking over this :D
• Dec 4th 2010, 07:31 PM
DrSteve
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).
• Dec 4th 2010, 08:19 PM
mybrohshi5
Thank you. Changes were corrected in post :D