Curve Integrals

May 2010
"The integral I is defined by

I=∫F.dr where F(x,y)=(x-y),(xy)

And C is the triangle with vertices (0,0), (1,0) and (1,3) traversed anticlockwise.

Calculate the line integral directly"

I don't know how to get started on this! Please help?


MHF Hall of Honor
Feb 2009
I'd rather use Green's Theorem.
BUT if you wish to do this directly you need to figure out the three lines parametrically.

From (0,0) to (1,0)
you can let y=0, x=t where 0<t<1
note that dy=0, dx=dt

From (1,0) to (1,3)
you can let y=t, x=1 where 0<t<3
here dy=dt, dx=0

Finally you have
(1,3) to (0,0)
you can let y=3t, x=t BUT 1<t<0 since you are heading to (0,0)
then dy=3dt, dx=dt
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Reactions: NoEyedClare
May 2010
The next part of the question is to verify using Green's Theorem. Thanks for that! I knew it involved parametric equations, just wasn't sure on how to set them up.