Solution Found!
Evaluating line integrals Evaluate the line integral for
Chapter 13, Problem 29E(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.
\(\varphi(x, y)=x+3 y ; C: \mathbf{r}(t)=\langle 2-t, t\rangle, \text { for } 0 \leq t \leq 2\)
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.
\(\varphi(x, y)=x+3 y ; C: \mathbf{r}(t)=\langle 2-t, t\rangle, \text { for } 0 \leq t \leq 2\)
ANSWER:Solution 29E
Step 1:
Given that
φ(x,y)=x+3y; C:r(t) = 〈2− t, t〉, for 0≤ t ≤ 2