Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 correct 3

Question

Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 correct 3560 13560 incorrect At least one of the answers above is NOT correct. (a) Find curl F (b) What does your answer to part (a) tell you about fo F dr where C is the circle (z-15)" + (y-5):= Inthe ru-plane,oriented clockwise? e) i C is any closed curve, what can you say about Sc F.dr? (d) Now let C be the haif circle (x15)(u-5 1 in the zy-plane with y >5, traversed trom (16,5) to (14,5), Find Sc F dF by using your result from (c) and considering C plus the line lep.6-113560 Note: You can eam partial credit on this problem

Explanation / Answer

C1:

for the line joining points (14,5),(16,5)

x=2t , y=5, z=0 ,7t8

r(t)= 2ti+5j+0k

F=(2z+2x3)i +(7y+2z+2sin(y3))j +(2x+2y+7ez^3)k

F(r(t))=(0+2(2t)3)i +(35+0+2sin(53))j +(2(2t) +5+7e0)k

F(r(t))=(0+16t3)i +(35+0+2sin(125))j +(4t +5+7)k

F(r(t))=(16t3)i +(35+2sin(125))j +(4t +12)k

r'(t)= 2i+0j+0k

C1F.dr=[7 to 8]F(r(t)) .r'(t) dt

C1F.dr=[7 to 8]((16t3)i +(35+2sin(125))j +(4t +12)k) .(2i+0j+0k ) dt

C1F.dr=[7 to 8][((16t3)*2) +((35+2sin(125))*0) +((4t +12)*0)] dt

C1F.dr=[7 to 8][32t3 +0+0] dt

C1F.dr=[7 to 8]32t3 dt

C1F.dr=[7 to 8]8t4

C1F.dr=8(84-74)

C1F.dr=8*1695

C1F.dr=13560

CF.dr+C1F.dr=0

CF.dr+13560=0

=>CF.dr=-13560

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