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Evaluating line integrals Evaluate the line
Chapter 13, Problem 30E(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.
\(\varphi(x, y, z)=x+y+z\); \(C: \mathbf{r}(t)=\langle\sin t, \cos t, t / \pi\rangle\), for \(0 \leq t \leq \pi\)
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.
\(\varphi(x, y, z)=x+y+z\); \(C: \mathbf{r}(t)=\langle\sin t, \cos t, t / \pi\rangle\), for \(0 \leq t \leq \pi\)
ANSWER:Solution 30E
Step 1:
Given that
φ(x,y,z) =(x + y + z); C:r(t) = 〈sin t, cos t,t /π 〉, for 0≤ t ≤2π