Subject : Calculus

QUESTION NO 3 a) [10] Verify Green's Theorem for of (ry? + z?) dax + (4x - 1) dy where C is shown below by (a) computing the line integral directly and (b) using Green's Theorem to compute the line integral. b) Find the work done by the force field F on a particle that moves along the curve C. [5] For. >. 2) = xyityzit xck C:rin) = nitritek (OSIsD) c) Show that the integral is independent of the path and find its value. [5] (@'my - " Jax + (- e'Ins) dy, where r and y are positive