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Scalar line integrals in the planea. Find a
Chapter 13, Problem 20E(choose chapter or problem)
Scalar line integrals in the plane
a. Find a parametric description for C in the form \(\mathbf{r}(t)=\langle x(t), y(t)\rangle\), if it is not given.
b. Evaluate \(\left|\mathbf{r}^{\prime}(t)\right|\).
c. Convert the line integral to an ordinary integral with respect to the parameter and evaluate it.
\(\int_{C}(2 x-3 y) d s\); C is the line segment from (-1,0) to (0,1) followed by the line segment from (0,1) to (1,0).
Questions & Answers
QUESTION:
Scalar line integrals in the plane
a. Find a parametric description for C in the form \(\mathbf{r}(t)=\langle x(t), y(t)\rangle\), if it is not given.
b. Evaluate \(\left|\mathbf{r}^{\prime}(t)\right|\).
c. Convert the line integral to an ordinary integral with respect to the parameter and evaluate it.
\(\int_{C}(2 x-3 y) d s\); C is the line segment from (-1,0) to (0,1) followed by the line segment from (0,1) to (1,0).
ANSWER:Solution 20E
Step 1
