HOMEWORK FOR MTH201- SUBMISSION DEADLINE: 30 NOVEMBER 2017 1. Use Greens' theorem to evaluate the line integral F.dr where F(zw) = (r-r'), (r' + rl, and C is the triangle bounded by y = 0, x = 3. and y = z, oriented clockwise. 2. Consider the line integral sin()co(r)dr+cos() siner)dy+d where C is the line segment from A(1,0,0) to B(0, 1,1) First show that the integral is independent from path and then calculate the integral by finding a potential function 3. Use Stokes' theorem to evaluate the line integral F.dr where Fir, y, a) +4j+k, and the closed curve C is obtained by cutting the cone ;-VET+ by the plane :-2, oriented counterclockwise as viewed from above 4. Use the divergence theore to find the flux of the vector field (r,y,) fi + rj + 'k outward through the surface of the sphere r2 +2 = a2 (a > 0). Date: Novenbser 20, 2017