## Calculus (3rd Edition)

$980000 \ J$
The force of one layer is equal to: $\ Force= \ Mass \times \ gravity = 9.8 \times (1000) \times 32 \Delta y \ N=313600 \Delta y \ N$ Therefore, the work done against can be computed as: $W=\int_{0}^{2.5} 313600 y \ dy \\=313600 [\dfrac{y^2}{2}]_{0}^{2.5} \\ =156800 [y^2]_{0}^{2.5} \\=156800 \times (2.5)^2$ By using a calculator, the required result is: $W \approx 980000 \ J$