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consider the vector field F(x,y,z)= < 2xyz, x 2 z, x 2 y +1 >. a) show that F is irrational (curl F equivalent to
consider the vector field F(x,y,z)=< 2xyz, x2z, x2y +1 >.
a) show that F is irrational (curl F equivalent to 0)
b) quote a theorem to conclude that F is conservative.
c) compute a potential function of F
d) compute the line integral of F along the curve C parametrized by r(t)= (t2, t4, t6 ), for 0
e) Let now F(x,y,z)= < 2xyz, x2z, x2y + 2zcos(z2+1) >. Compute the line integral of F
along the curve parameterized by r(t)= (t2, t4, t6), for 0
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