Correct option is (4) 126 J
\(w = \int dw . \int f.ds\)
\(w = 2\int\limits_{(1, 1)}^{(2, 4)} (xy^2 \hat i + yx^2 \hat j).(dx\hat i + dy\hat j)\)
\(= 2 \left[\frac{x^2y^2}{2} + \frac{y^2 x^2}2 \right]_{(1, 1)}^{(2, 4)}\)
\(= 2 \left[x^2 y^2\right]_{(1,1)}^{(2, 4)}\)
\(= 2[4 \times 16] - 2[1]\)
\(= 2 (64 - 1)\)
\(= 2 \times 63\)
\(= 126\ J\)
