Question

Verify Green’s theorem for      C (xy y2 )dx x2dy where C is the boundary of the common area between y  x2 and y  x .

Answer 1

We shall find the points of intersection of y = x and y = x².

Equating the R.H.S.

∴ x = x2 ⇒ x – x2 = 0

x (1 – x) = 0

x = 0, 1

∴ y = 0, 1 and hence (0, 0), (1, 1) are the points of intersection.

We have Green’s theorem in a plane,