3. a) Consider the vector field F(x, y, z) = (2xy2 z, 2x 2 yz,x2 y 2 ) and the curve r(t) = (sin t,sin t cost, cost) on theinterval [ ? 4 , 3? 4 ]. Calculate R C F · dr using the definitionof the line integral. [5] b) Find a function f : R 3 ? R so that F= ?f. [5] c) Verify your answer from (a) using (b) and theFundamental Theorem for Line Integrals. [5]
