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An object has a displacement from positi...

An object has a displacement from position vector `vec(r )_(1)=(2hat(i)+3hat(j))m` to `vec(r )_(2)=(4hat(i)+6hat(j))m` under a force `vec(F)=(3x^(2)hat(i)+2y hat(j))N`. Find the work done by this force.

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`W = int_(vec(r)_(i))^(vec(r)_(f)) vec(F). d vec(r) = int_(vec(r)_(1))^(vec(r)_(2)) (3 x^(2) hat(i) + 2 y hat(j)).(d x hat(i) + dy hat(j) + dz hat(k))`
`= int_(vec(r)_(1))^(vec(r)_(2)) (3x^(2) dx + 2y dy) = (x^(3) + y^(2))_((2,3))^((4,6)) = 83 J`
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