Let C be the curve which is the union of two line segments, the first going from (0, 0) to (3, -3) and the second going from (3, -3) to (6, 0).

Computer the line integral http://hosted2.webwork.rochester.edu...0d280e0121.png.

Thankyou.

Printable View

- Nov 23rd 2008, 03:07 PMiwonderline integral
Let C be the curve which is the union of two line segments, the first going from (0, 0) to (3, -3) and the second going from (3, -3) to (6, 0).

Computer the line integral http://hosted2.webwork.rochester.edu...0d280e0121.png.

Thankyou. - Nov 24th 2008, 09:33 AMMoo
Hello,

Make a parametrization.

Equation of line (0,0) to (3,-3) is y=-x.

So make x=t and y=-t and substitute in the integral !

for t going from 0 to 3 (since it's x)

Equation of line (3,-3) to (6,0) is y=x-6.

x=t and y=t-6

for t going from 3 to 6.

So this should give for the first one :

$\displaystyle \int_0^3 -3+3 ~ dt$

(note that since y=-t, dy=-dt)