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Mass and Density  Two Dimenstions
Imagine a flat plate which occupies the region below the curve y = f(x), f(x) ≥ 0, from x = a to x = b. If its density per unit area is a constant ρ gm/cm^{2}, then its mass is the product of the density and area, Suppose instead that the density depends on the value of x, ρ(x). Consider a vertical strip of the plate of infinitesimal width Δx (Figure 6.6.3). On the strip between x and x + Δx, the density is everywhere infinitely close to ρ(x), so Δm ≈ ρ(x) ΔA ≈ ρ(x) f(x) Δx (compared to Δx). Figure 6.6.3 By the Infinite Sum Theorem,


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