## Calculus (3rd Edition)

$3920 \ J$
The force of one layer is equal to: $\ Force= \ Mass \times \ gravity = 78.4 \Delta y \ N$ The work done on the $i$th segment is the sum of the $W_i$; that is, $W=\Sigma_{j=1}^N W_i \approx \Sigma_{j=1}^N 78.4 y_j \Delta y$ Therefore, the work done when $N \to \infty$ can be computed as: $W=\int_{0}^{10} 78.4 \ y \ dy \\=39.2 [y^2]_{0}^{10} \\ =3920 \ J$