Physics Question from JEE Main 2025 · 23 January, Shift 1

A force $\vec{f} = x^2 y \, \hat{i} + y^2 \, \hat{j}$ acts on a particle in a plane $x + y = 10$. The work done by this force during a displacement from $(0,0)$ to $(4\,\text{m}, 2\,\text{m})$ is _____ Joule (round off to the nearest integer).