Calculating work done by a force field using Green's Theorem on a triangle

[kasse]

Homework Statement

Use Green's Theorem to calculate the work done by the force field

F = <5x²y³, 7x³y²>

in moving a particle counterclockwise once around the triangle with vertices (0, 0), (3, 0) and 0, 6).



2. The attempt at a solution

I must integrate 6x²y² over the triangle, right? I then get 1944 as the answer, but the correct answer is 972/5. What is wrong?

 

[Dick]

Yep, you got it set up all right. But I do get 972/5 for the double integral of 6*x^2*y^2 over the triangle. Check that again. Post how you worked it out if you can't get it.

 

[kasse]

Yep, you got it set up all right. But I do get 972/5 for the double integral of 6*x^2*y^2 over the triangle. Check that again. Post how you worked it out if you can't get it.

OK, i integrate with respect to y first, which gives 2x^2*y^3. The limits are y=0 and y=2x, so I now have to integrate 16x^5 with respect to x. This gives (8/3)x^6, and the limits are x=0 and x=3, so that the answer is 1944.

 

[Dick]

y=2x isn't one of the sides of your triangle. y=6-2x is. Draw a picture.

 

[kasse]

Lol, thanks!