MATH-2221 Lecture 39: 7.6 cont

p d r where F (3 sin z,4 cos y, zz) and C s the path given by r(t) ge, 3t) for 0

Let F(x, y, z) - xi + yj + zk. Evaluate the integral of F along each of the following paths. (a) c(t) = (3t, 3t, 30, 0 ts 1 (b) c(t)-(2 cos(t), 2 sin(t), 0), 0 s t 67 (c) c(t) = (2 sin(t), 0, 2 cos(t)), 0 t 67 (d) c(t) = (3t2, t, 2t3), -1 t 2

Consider F and C below F(x, y) = 9xy2 i + 9x2yj C: r(t)-〈 t + sin( nt), t + cos( (a) Find a function f such that F = f(x, y) = nt)), 0 t 1 f. (b) Use part (a) to evaluateVf dr along the given curve C