Line Integral - Vector Calculus

[cristina89]

Homework Statement

Calculate the line integral:
f(x,y) = (x² - 2xy)î + (y² - 2xy)j, between the points (-1,1) and (1,1) along the parabola y = x².
(resp: -14/15)


The attempt at a solution
I thought something like this: substitue y = x², and then integrate de f(x,y). And then evaluate from -1 to 1, but it didn't work, obviously. How should I start solving this? I think I didn't get the concept about this kind of exercise...

 

[HallsofIvy]

If it didn't work then you must have made an error in the integrall. What, exactly, did you do?

The integral of this will be [itex]\int (x^2 - 2xy)dx+ (y^2- 2xy)dy[//itex]. Did you remember to put dy in terms of x also?

 

[cristina89]

If it didn't work then you must have made an error in the integrall. What, exactly, did you do?

The integral of this will be [itex]\int (x^2 - 2xy)dx+ (y^2- 2xy)dy[//itex]. Did you remember to put dy in terms of x also?

Ahh, that's exactly what I was forgetting! Thank you!