In Exercises 45 and 46, evaluate for each curve.Discuss the orientation of the curve and

Chapter 15, Problem 46

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In Exercises 45 and 46, evaluate \(\int _C F \cdot\ dr\) for each curve. Discuss the orientation of the curve and its effect on the value of the integral.

\(F(x,\ y)=x^2yi+xy^{3/2}j\)

(a) \(r_1(t)=(t-1)i+t^2j,\ \ \ 0\ \leq\ t\ \leq\ 2\)

(b) \(r_2(t)=(1+2 \cos t)i+(4 \cos^2 t)j,\ \ \ 0\ \leq\ t\ \leq\ \pi/2\)

Text Transcription:

int _C F cdot dr

F(x, y) = x^2 yi + xy^3/2 j

r_1 (t) = (t+1)i + t^2 j, 0 leq t leq 2

r_2 (t) = (1 + 2 cos t)i + (4 cos^2 t)j, 0 leq t leq pi/2

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