Question

Verify Green’* theorem in the plane for ∫c{(xy + y2)dx + x2dy} where C is the closed curve of the region bounded by y = x and y = x2.

Answer 1

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

Equating the R.H.*.

∴ 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’* theorem in a plane,