Let F(x, y, z) = xi + yj + zk. Evaluate the integral of F along...
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Let F(x, y, z) = xi + yj + zk. Evaluate the integral of F along each of the following paths. (a) c(t) = (3t, 3t, 3t), 0 ≤t≤ 1 (b) c(t) = (2 cos(t), 2 sin(t), 0), (c) c(t) = (2 sin(t), 0, 2 cos(t)), 0 ≤ t ≤ 6π 0 ≤ t ≤ 6π (d) c(t) = (3t², t, 2t³), -1 ≤t≤ 2 Let F(x, y, z) = xi + yj + zk. Evaluate the integral of F along each of the following paths. (a) c(t) = (3t, 3t, 3t), 0 ≤t≤ 1 (b) c(t) = (2 cos(t), 2 sin(t), 0), (c) c(t) = (2 sin(t), 0, 2 cos(t)), 0 ≤ t ≤ 6π 0 ≤ t ≤ 6π (d) c(t) = (3t², t, 2t³), -1 ≤t≤ 2
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