In Exercises 45 and 46, evaluate for each curve.Discuss the orientation of the curve and
Chapter 15, Problem 46(choose chapter or problem)
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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