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MTH 252 Integral Calculus Chapter 6 – Integration Section 6.1 – An Overview of the Area Problem Copyright © 2005 by Ron Wallace, all rights reserved.

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Area: Inscribed Regular Polygon r n r n 2 sin 2 2 AnA2 tripoly

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Area: Circle r L’Hôpital’s Rule

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The Area Problem Given a continuous non-negative function f(x) over an interval [a, b]; find the area bounded by f(x), the x-axis, x=a, & x=b. x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 x0x0 x7x7 a1a1 a2a2 a3a3 a4a4 a5a5 a6a6 a7a7

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The Area Problem Given a continuous non-negative function f(x) over an interval [a, b]; find the area bounded by f(x), the x-axis, x=a, & x=b. x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 x0x0 x7x7 a1a1 a2a2 a3a3 a4a4 a5a5 a6a6 a7a7

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Example Approximate the area under f(x)=sin x over [0, ] using 4 rectangles and left endpoints. a2a2 a3a3 a4a4 NOTE: Actual area is 2.0.

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