# Line Integrals

1. Dec 9, 2011

### p0tat0phun

1. The problem statement, all variables and given/known data
The problem is given in the following image.
http://img46.imageshack.us/img46/2972/lskfjsf.png [Broken]

2. Relevant equations
∫h(r)*dr = ∫h[r(u)]*r'(u)du

3. The attempt at a solution
I was able to figure out plugging in (t^2+3) at every x and sin(1/2πt) at every y. I then set up the dot product of the substituted equation and r'(u)du (2t + 1/2πcos(1/2πt)). The problem is, the integral ends up being much to complex to work by hand since I'm not allowed to use a calculator for this problem. So I was wondering if there was an easier way to work this problem out?

Last edited by a moderator: May 5, 2017
2. Dec 9, 2011

### LCKurtz

Think about why the first part asked you to find f(x,y) whose gradient is the given vector field. Perhaps you can use that f(x,y) somehow, hint, hint.

Last edited by a moderator: May 5, 2017
3. Dec 9, 2011

### p0tat0phun

Okay, so I found f(x,y) to be:
3x + e^x*y^2 + 3e^x*y + 2e^x + y^2
But I'm still confused on where to continue with that.

4. Dec 9, 2011

### LCKurtz

Your text should have a theorem about evaluating line integrals when you have a potential function f(x,y), and that is the whole point of this problem.