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Solution: Scalar line integrals in the planea. Find a
Chapter 13, Problem 18E(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.
\(\int_{C}(x y)^{1 / 3} d s\); C is the curve \(y=x^{2}\), for \(0 \leq x \leq 1\)
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.
\(\int_{C}(x y)^{1 / 3} d s\); C is the curve \(y=x^{2}\), for \(0 \leq x \leq 1\)
ANSWER:Solution 18E
Step 1
