If C is the triangle of vertices (0,0), (1,0) and (1,1) oriented in direction anti-clockwise

Solution:

Correct ????

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- Apr 26th 2009, 03:12 PMApprentice123Theorem of Green
If C is the triangle of vertices (0,0), (1,0) and (1,1) oriented in direction anti-clockwise

Solution:

Correct ???? - Apr 26th 2009, 03:24 PMCalculus26
Not quite

Green's Thm --- Line Integral = integral(dg/dx-df/dy) over the region enclosed by the C

you computed dg/dx-df/dy correctly = 1

so the line integral is the area of the triangle then which is 1/2 - Apr 26th 2009, 03:28 PMApprentice123
- Apr 26th 2009, 03:30 PMJester
- Apr 26th 2009, 03:33 PMApprentice123
- Apr 26th 2009, 03:58 PMCalculus26
I know you know how to set up a double integral otherwise you wouldn't be doing line integrals and green's theorem.

the equation of the line from (0,0) to (1,1)

is y = x

so y varies from 0 to x as x varies from 0 to 1 - Apr 26th 2009, 04:03 PMApprentice123Of course. thanks
- Apr 26th 2009, 04:09 PMJester
Here is the region of interest. In order to set up

then we would need the following

.

Since the inner integral involves then the curve to cuve in in the direction and in your case and hence the inside integral . Then outer integral is point to point and since the outer involves then we are moving in the direction and from the picture of the region it and hence the outer integral of

Hope that helps. - Apr 26th 2009, 04:18 PMApprentice123