A three coulomb charge moves from the point (0, -2, -5) to the point (5, 1, 2) in an electric field expressed as $$\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k}$$ N/C. The work done in moving the charge is _______ J.

$$W = q \int_{A}^{B} \vec{E} \cdot d\vec{r}$$

$$\vec{E} \cdot d\vec{r} = (2x\hat{i} + 3y^2\hat{j} + 4\hat{k}) \cdot (dx\hat{i} + dy\hat{j} + dz\hat{k}) = 2x\,dx + 3y^2\,dy + 4\,dz$$

$$W = 3 \int_{A}^{B} (2x\,dx + 3y^2\,dy + 4\,dz)$$

$$W = 3 \left[ \int_{0}^{5} 2x\,dx + \int_{-2}^{1} 3y^2\,dy + \int_{-5}^{2} 4\,dz \right]$$

$$W = 3 [25 + 9 + 28]$$

$$W = 186 \text{ J}$$