1. ## Line integral help

am stuck on the integration part, so far I have
x = cost , y = sint

dx = -sint dt dy = cost dt

$\displaystyle \int ( xy^{2}) dx + ( x^{2}y + 2x) dy$ subbing in the values for x,y, dx and dy

i get

$\displaystyle \int^{2\pi}_{0} ( -cost sin^{3}t + cos^{3}t sint + 2cos^{2}t ) dt$

how do I simply / integrate this expression ?

2. ## Re: Line integral help

You can integrate the first two terms using substitutions, and the third using a double angle identity.

3. ## Re: Line integral help

I am puzzled by this. The given problem, to integrate $\displaystyle x^2ydx+ (x^2y+ 2x)dy$, I presume around the unit circle, is not difficult but it is a typical "Calculus III" or "Calculus of several variables" problem while the part you are stuck on is standard "Calculus I". You need a review! Go back to your Calculus I text and look at the chapter on trig integrals.

4. ## Re: Line integral help

Have you gotten an answer for this yet? Have you tried using Green's Theorem yet?

5. ## Re: Line integral help

Yes

$\displaystyle (\frac{1}{4} sin^{4}t )^{2\pi}_{0} + \frac{1}{4}cos^{4}t)^{2\pi}_{0} + 2 [ \frac{1}{4} sint2t +\frac{t}{2} )^{2\pi}_{0}$

= $\displaystyle 2\pi$
using green's theorem i get same

6. ## Re: Line integral help

Be VERY careful with your signs. You have sign errors in the first two terms...