2. If C is a smooth curve given by a vector function r(t), a ? t ? b, and v is a constant vector, show that $\int_C v \cdot dr = v \cdot [r(b) - r(a)]$ Proof:
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Step 1: Since v is a constant vector, we can take it out of the integral: $$ \int_C \mathbf{v} \cdot d\mathbf{r} = \mathbf{v} \cdot \int_C d\mathbf{r} $$ Show more…
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