1 answer

1. (25 pts] Let F(x, y, z) = (2xy4 +25)i + (4.x²y3 + 2yz3)j + (5x24...

Question:

1. (25 pts] Let F(x, y, z) = (2xy4 +25)i + (4.x²y3 + 2yz3)j + (5x24 + 3y2 -2)k and let C be the curve given parametrically by

1. (25 pts] Let F(x, y, z) = (2xy4 +25)i + (4.x²y3 + 2yz3)j + (5x24 + 3y2 -2)k and let C be the curve given parametrically by r(t) = (3t+1)i + t?j + 5tk for 0 <t<1. Evaluate the line integral [F F. dr

Answers

given that, F43) = ax +3%); + (1+233) + (57+93 at first we have to show that the vector field is conservative he know that, FHequee p is a conser vorive toneel tield then there exist a sealan potential o such that F=79 Now do= a dx + aq dy te da ZgodWhen t=0. we get 0 the point (( 3110) +1, iel (1,0,0) E 741 = (sttwittstatus 165)10) ) - and when t=1, we get the point 15))

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