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

Area: Inscribed Regular Polygon r         n r n   2 sin 2 2  AnA2 tripoly

Area: Circle r  L’Hôpital’s Rule

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

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

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.