Question

(6) Verify Green's theorem
for integral
[[(3x2 – 8y2)dx + (4y - 6xy)dy] where C is
boundary of region bounded by straight lines
x = 0, y = 0 and x + y = 1.​

Answer 1

Step-by-step explanation:

We'll use Green's theorem to calculate the area bounded by the curve. Since C is a counterclockwise oriented boundary of D, the area is just the line integral of the vector field F(x,y)=12(−y,x) around the curve C parametrized by c(t).

Green's theorem only applies to curves that are oriented counterclockwise. If you are integrating clockwise around a curve and wish to apply Green's theorem, you must flip the sign of your result at some point.

Answer 2

boundary off region foundation