MAC 2147 Lecture 1: KIC Document 0058

Comparing Functions Winch of the following vector- valued functions represent the same graph?

(a) r(t)=(–3 cos t + l)i + (5 sin t + 2)j 4 + 4k

(b) r(t)=4i + (–3 cos t + l)j + (5 sin t + 2)k

(c) r(t)=(3 cos t– l)i + (–5 sin t –2)j + 4k

(d) r(t)=(–3 cos 2t + l)i + (5 sin 2t + 2)j + 4k

Evaluate the line integral \int_C \mathbf{F}\cdot d\mathbf{r}, where \mathbf{F}(x,y,z) = 4 \sin x \mathbf{i} + 2 \cos y \mathbf{j} + 5x z\mathbf{k} and C is given by the vector function \mathbf{r}(t) = t^3 \mathbf{i} - t^2 \mathbf{j} + t^1 \mathbf{k} , \quad 0 \le t \le 1.