Line integral uncertain about direction.

[aleee]

Homework Statement

Evaluate \int[(3x-y)dx-xdy] where C consist of the parabola y=x^2 from (0,0) to (1,1) and then the line segment from (1,1) to (0,1)

Homework Equations

The Attempt at a Solution

i did the integral of the y=x^2
parametrized
x=t
y=t^2
from 0 to 1
then i got my 1/2
but for the line segment do i just take the the integral using
x=t
y=1
but for the interval do i use 0 to 1 or 1 to 0

 

[Dick]

You want to go from (1,1) to (0,1) along (t,1). That makes it t=1 to t=0, right?

 

[aleee]

so would i get \int_1^0\\(3t-1)dt
and would i just integrate it like that
i wouldn't require a negative because its a parametric correct?

 

[Dick]

so would i get \int_1^0\\(3t-1)dt
and would i just integrate it like that
i wouldn't require a negative because its a parametric correct?

Sure. You don't have to add any extra signs. Just work out what it is and add it to your first path.

 

[aleee]

thanks for the help!