Suppose F ( x y ) = ? y i + x j and C is the line segment from point P = 4 0 to

Question

SupposeF(xy)=?yi+xjandCis the line segment from pointP=40toQ=03.

(a) Find a vector parametric equationr(t)for the line segmentCso that pointsPandQcorrespond tot=0andt=1, respectively.
r(t)=

(b) Using the parametrization in part (a), the line integral ofFalongCis
CFdr=abF(r(t))r(t)dt=abdt
with limits of integrationa=andb=

(c) Evaluate the line integral in part (b).


(d) What is the line integral ofFaround the clockwise-oriented triangle with corners at the origin,P, andQ? Hint: Sketch the vector field and the triangle.

Explanation / Answer

COULD YOU PLEASE TAKE THE IMAGE PROPERLY BECAUSE r(t) .. ARE NOT SEEN PROPERLY..

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