3132 Use a CAS to evaluate the line integrals along the given curves. (a) Cx7y3 dsC : x

Chapter 15, Problem 32

(choose chapter or problem)

use a CAS to evaluate the line integrals along the given curves.

(a)  \(\int_{C} x^{7} y^{3} d s\)

\(C: r(t)=e^{t} i+e^{-t} j \quad(0 \leq t \leq \ln 2)\)

(b) \(\int_{C} x^{5} z d x+7 y d y+y^{2} z d z\)

\(\mathrm{C}: \mathrm{r}(\mathrm{t})=\mathrm{t} \mathrm{i}+\mathrm{t}^{2} \mathrm{j}+\ln \mathrm{t} \mathrm{k} \quad(1 \leq \mathrm{t} \leq \mathrm{e})\)

Equation Transcription:

Text Transcription:

integral_C x^7 y^3 ds

C: r(t) = e^t i + e^-t j   (0 leq t leq ln 2)

integral_C x^5 z dx + 7y dy + y^2 z dz

C: r(t) = t i + t^2 j + ln t k    (1 leq t leq e)

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