Solved: Evaluating a Line Integral of a Vector Field In Exercises 1124, find the value

Chapter 15, Problem 12

(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.)

\(\mathbf{F}(x, y)=y e^{x y} \mathbf{i}+x e^{x y} \mathbf{j}\)

(a) \(\mathbf{r}_{1}(t)=t \mathbf{i}-(t-3) \mathbf{j}, \quad 0 \leq t \leq 3\)

(b) The closed path consisting of line segments from (0, 3) to (0, 0), from (0, 0) to (3, 0)

Text Transcription:

int_C F cdot dr

F(x, y) = ye^{xy}i + xe^{xy}j

r_1 (t) = ti - (t - 3)j,     0 leq t leq 3

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