Solution: Line integrals Evaluate the line integral using a

Chapter 13, Problem 43E

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QUESTION:

Evaluate the following line integrals using a method of your choice.

\(\oint_{C} \mathbf{F} \cdot d \mathbf{r}\), where \(\mathbf{F}=\left\langle 2 x y+z^{2}, x^{2}, 2 x z\right\rangle\) and C is the circle \(\mathbf{r}(t)=\langle 3 \cos t, 4 \cos t, 5 \sin t\rangle\), for \(0 \leq t \leq 2 \pi\).

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QUESTION:

Evaluate the following line integrals using a method of your choice.

\(\oint_{C} \mathbf{F} \cdot d \mathbf{r}\), where \(\mathbf{F}=\left\langle 2 x y+z^{2}, x^{2}, 2 x z\right\rangle\) and C is the circle \(\mathbf{r}(t)=\langle 3 \cos t, 4 \cos t, 5 \sin t\rangle\), for \(0 \leq t \leq 2 \pi\).

ANSWER:

Solution 43EThe v

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