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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.

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Area Between Two Curves

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  1. Area Between Two Curves Calculus

  2. 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

  3. 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

  4. 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

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

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

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

  8. 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

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

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

  11. Example #2

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

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

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

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

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