Physics - W.E.P. Question with Solution | TestHub

The work done by a variable force $\vec{F}$ is given by $W=\int \vec{F}\cdot d\vec{r}$. Here, $\vec{F}=(2x\hat{i}+3y^2\hat{j})$ and $d\vec{r}=dx\hat{i}+dy\hat{j}$.$$W={\int }_{(0,0)}^{(3,4)}(2xdx+3y^{2}dy)={\int }_0^{3}2xdx+{\int }_0^{4}3y^{2}dy$$ $$W=[x^2{]}_0^3+[y^3{]}_0^4=(3^2-0^2)+(4^3-0^3)=9+64=73\text{ J}$$