In Section 6.2, we computed the volume V of a solid as the integral of cross-sectional
Chapter 9, Problem 66(choose chapter or problem)
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 12. (a) Explain the following approximation for small y: V (y + y) V (y) A(y) y 8 (b) Use Eq. (8) to justify the differential equation dV /dy = A(y). Then derive the formula V = b a A(y) dy Volume of slice is V(y + y) V(y) A(y)y Area of cross section is A(
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