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Home Applications of the Integral Infinite Sum Theorem Area Between Two Curves  
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Area Between Two Curves
We shall use the Infinite Sum Theorem several times in this chapter. As a first illustration of the method, we derive again the formula from Chapter 4 for the area of the region between two curves, shown in Figure 6.1.3. Figure 6.1.3 AREA BETWEEN TWO CURVES where f and g are continuous and f(x) ≤ g(x) for a ≤ x ≤ b. The justification of a definition resembles the proof of a theorem, but it shows that an intuitive concept is equivalent to a mathematical one. We shall now use the Infinitive Sum Theorem to give a justification of the formula for the area between two curves. JUSTIFICATION ΔA x [g(x)  f(x)] Δx (compared to Δx). The infinite sum theorem now shows that A(a, b) is the integral of g(x)  f(x) from a to b. Figure 6.1.4


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