Chapter 16.1, Problem 55E

Cylinders Let S be the solid in ${ℝ}^3$between the cylinder z = f(x) and the region, where f(x) ≥ 0 on R. Explain why ${\displaystyle {\int }_c^d{\displaystyle {\int }_a^{b}f\left(x\right)dxdy}}$ equals the area of the constant cross section of S multiplied by (d – c), which is the volume of S.