Unformatted text preview: the height is determined by the left side of the rectangle touching the curve. Definition: Let a function f be defined on the interval [a, b] and let f(x)> 0 for all x in [a,b]. Then the area A of the region that lies between the graph of f and the xaxis is the limit of the sum of the areas of approximating rectangles: 1 2 1 [ ( ) ( ) ... ( ) ] lim lim lim ( ) n n n i i n n n i A R f x x f x x f x x f x x →∞ →∞ →∞ = = = Δ + Δ + + Δ = Δ & where b a x nΔ = and i x a i x = + Δ , provided the limit exists. Try exercises 2, 4, 18, 24 on pages 364365 in your text....
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 Spring '11
 Teague
 Calculus, Angles, Rectangle, rectangles

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