Question

what is the work done in moving an object around a circle C in the xy plane, if the circle has radius 5 and is centered at the origin and the force field is F=(5x^2+3y+5z)i+(7yx^3+4x-z^2)j+(9x+8y^2-14z)k?

Answer 1

by using mathematica..

Answer 2

is that zero

Answer 3

i'm not sure...but i also get zero...actually,is it like this :
LineInt[F_, r_, a_, b_] :=\[ \int\limits_{a}^{b}F \delta _{t}r dt\]
r = {5 Cos[t], 5 Sin[t], 0};
F =\[ {5 x ^{2} + 3 y + 5 z, 7 x^{3} y + 4 x - z^{2}, 9 x + 8 y^{2} - 14 z};\]
a = 0; b = 2pi;
LineInt[F, r, a, b]

Answer 4

typo...F=\[\left\{ 5x^{2}+3y+5z,7x^{3}y+4x-z^{2},9x+8y^{2}-14z \right\}\]