Line integrals of vector fields in the plane

Chapter 13, Problem 37E

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QUESTION:

Given the following vector fields and oriented curves C, evaluate \(\int_{C} \mathbf{F} \cdot \mathbf{T} d s\).

\(\mathbf{F}=\frac{\langle x, y\rangle}{\left(x^{2}+y^{2}\right)^{3 / 2}}\) on the curve \(\mathbf{r}(t)=\left\langle t^{2}, 3 t^{2}\right\rangle\), for \(1 \leq t \leq 2\)

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QUESTION:

Given the following vector fields and oriented curves C, evaluate \(\int_{C} \mathbf{F} \cdot \mathbf{T} d s\).

\(\mathbf{F}=\frac{\langle x, y\rangle}{\left(x^{2}+y^{2}\right)^{3 / 2}}\) on the curve \(\mathbf{r}(t)=\left\langle t^{2}, 3 t^{2}\right\rangle\), for \(1 \leq t \leq 2\)

ANSWER:

Solution 37EStep 1

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