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AP®︎/College Calculus BC

Course: AP®︎/College Calculus BC > Unit 8

Lesson 6: Finding the area between curves that intersect at more than two points
Math
AP®︎/College Calculus BC
Applications of integration
Finding the area between curves that intersect at more than two points
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Area between curves that intersect at more than two points (calculator-active)

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Problem

Let f, left parenthesis, x, right parenthesis, equals, 2, cosine, left parenthesis, start fraction, pi, x, divided by, 3, end fraction, right parenthesis and g, left parenthesis, x, right parenthesis, equals, 2, dot, start fraction, 8, minus, x, divided by, x, plus, 6, end fraction, minus, 1. Let R and S be the two regions enclosed by the graphs of f and g as shown in the graph.
Find the sum of the areas of regions R and S.
Use a graphing calculator and round your answer to three decimal places.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
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