"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?
"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?
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