Now answered: Evaluating a Line Integral of a Vector Field In Exercises 1124, find the

Chapter 15, Problem 22

(choose chapter or problem)

In Exercises 11 - 24, find the value of the line integral

\(\int_{C} \mathbf{F} \cdot d \mathbf{r}\).

(Hint: If F is conservative, the integration may be easier on an alternative path.)

\(\mathbf{F}(x, y, z)=-y \mathbf{i}+x \mathbf{j}+3 x z^{2} \mathbf{k}\)

(a) \(\mathbf{r}_{1}(t)=\cos t \mathbf{i}+\sin t \mathbf{j}+t \mathbf{k}, \quad 0 \leq t \leq \pi\)

(b) \(\mathbf{r}_{2}(t)=(1-2 t) \mathbf{i}+\pi t \mathbf{k}, \quad 0 \leq t \leq 1\)

Text Transcription:

int_C F cdot dr

F(x, y, z) = -yi + xj + 3xz^{2}k

r_1 (t) = cos ti + sin tj + tk,     0 leq t leq pi

r_2 (t) = (1 - 2t)i + pi tk,     0 leq t leq 1