Area Between Two Curves

Area Between Two Curves Calculus

Think WAY back… • The diagram shows a green piece of square carpeting. A hole is being cut out of the carpeting for a column 6' in diameter. How many square feet of carpeting are shown in this diagram? Round answer to the nearest tenth of a square foot. http://www.regentsprep.org/regents/math/ALGEBRA/AS1/PracArea.htm

Think WAY back… 324 sq. ft. • What is the area of the square? • What is the area of the circle? • How do we find the area of the green section? 28.3 sq. ft. 324 - 28.3 = 295.7

Riemann Sums… http://mathoverflow.net/questions/16184/can-a-limit-to-zero-of-a-limit-to-zero-assume-theyre-both-going-at-the-same-rate

Followed by Definite Integrals… http://www.msstate.edu/dept/abelc/math/integral_area.png

NOW…The Area Between Two Curves Area under f(x) Area under g(x) http://thesaurus.maths.org/mmkb/media/png/AreaBetweenCurves.png

Process: http://tutorial.math.lamar.edu/AllBrowsers/2413/AreaBetweenCurves.asp

Example #1 • Determine the area of the region enclosed by and • The limits of integration will be the intersection points of the two curves. In this case x=0 and x=1. http://tutorial.math.lamar.edu/AllBrowsers/2413/AreaBetweenCurves.asp

Example #1 http://tutorial.math.lamar.edu/AllBrowsers/2413/AreaBetweenCurves.asp

Example #2 • Determine the area of the region bounded by and http://tutorial.math.lamar.edu/AllBrowsers/2413/AreaBetweenCurves.asp

Example #2

Example #3 • Determine the area of the region bounded by http://tutorial.math.lamar.edu/AllBrowsers/2413/AreaBetweenCurves.asp

Example #3 http://tutorial.math.lamar.edu/AllBrowsers/2413/AreaBetweenCurves.asp

Homework Page 454 #1-6, 19-21, 23-25, 27, 28

Area Between Two Curves