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Solution: Evaluating line integrals Evaluate the line
Chapter 13, Problem 32E(choose chapter or problem)
QUESTION:
Evaluate the line integral \(\int_{C} \nabla \varphi \cdot d \mathbf{r}\) for the following functions \(\varphi\) and oriented curves C in two ways.
\(\varphi(x, y, z)=x y+x z+y z\); \(C: \mathbf{r}(t)=\langle t, 2 t, 3 t\rangle\), for \(0 \leq t \leq 4\)
Questions & Answers
QUESTION:
Evaluate the line integral \(\int_{C} \nabla \varphi \cdot d \mathbf{r}\) for the following functions \(\varphi\) and oriented curves C in two ways.
\(\varphi(x, y, z)=x y+x z+y z\); \(C: \mathbf{r}(t)=\langle t, 2 t, 3 t\rangle\), for \(0 \leq t \leq 4\)
ANSWER:Solution 32EStep 1:Given that(x,y,z)=xy+xz+yz; C:r(t) = t, 2t, 3t , for 0 t 4