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

Explanation

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