In Section 6.2, we computed the volume V of a solid as the integral of cross-sectional area. Explain this formula in terms of differential equations. Let V(y) be the volume of the solid up to height y, and let A(y) be the cross-sectional area at height y as in Figure 17.

(a) Explain the following approximation for small Δy:

(b) Use Eq. (11) to justify the differential equation dV/dy = A(y). Then derive the formula

Transcribed Image Text:

V(y+Ay) - V(y) ≈ A(y) Ay