Area Between Two Curves Calculus. Think WAY back…

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Presentation transcript:

Area Between Two Curves Calculus

Think WAY back…

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.

Think WAY back… What is the area of the square? What is the area of the circle? How do we find the area of the green section?

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

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

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

Then: Definite Integrals…

NOW…The Area Between Two Curves Area under f(x)

NOW…The Area Between Two Curves Area under g(x)

NOW…The Area Between Two Curves

Process:

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.

Example #1

Example #1

Example #1

Example #2 Determine the area of the region bounded by and

Example #2

Example #3 Determine the area of the region bounded by