Question

(1 point) Suppose F⃗ (x,y)=−yi⃗ +xj⃗ F→(x,y)=−yi→+xj→ and CC is the line segment from point P=(4,0)P=(4,0) to Q=(0,5)Q=(0,5). (a) Find a vector parametric equation r⃗ (t)r→(t) for the line segment CC so that points PP and QQ correspond to t=0t=0 and t=1t=1, respectively. r⃗ (t)=r→(t)= <4,0>+t<-4,5> (b) Using the parametrization in part (a), the line integral of F⃗ F→ along CC is ∫CF⃗ ⋅dr⃗ =∫baF⃗ (r⃗ (t))⋅r⃗ ′(t)dt=∫ba∫CF→⋅dr→=∫abF→(r→(t))⋅r→′(t)dt=∫ab 20 dtdt with limits of integration a=a= 0 and b=b= 1 (c) Evaluate the line integral in part (b). 20 (d) What is the line integral of F⃗ F→ around the clockwise-oriented triangle with corners at the origin, PP, and QQ

Answer 1

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