# An object has a displacement from position vector $\vec{r_{1}}&space;=&space;(2\hat{i}+3\hat{j})m$ to $\vec{r_{2}}&space;=&space;(4\hat{i}+6\hat{j})m$ under a force $\vec{F}&space;=&space;(3x^{2}\hat{i}+2y\hat{j})N$ then work done by the force is (a) 24 J (b) 33 J (c) 83 J (d) 45 J

Work done is given by,

$W&space;=&space;\int\vec{F}.&space;(dx\hat{i}&space;+&space;dy\hat{j})$

$W&space;=\int_{2}^{4}3x^{2}dx&space;+&space;\int_{3}^{6}2y&space;dy$

$W&space;=&space;\left&space;[&space;x^{3}&space;\right&space;]_{2}^{4}&space;+&space;\left&space;[&space;y^{2}&space;\right&space;]_{3}^{6}$

W = (64 – 8) + (36 – 9)

W = 56 + 27

We get,

W = 83 J