Explanation Given: Curves as f ( x ) = 2 x and g ( x ) = 6 − x . Formula Used: The area between curves is the area between the curve f ( x ) and curve g ( x ) on an interval [ a , b ] is given as follows A = ∫ a b | f ( x ) − g ( x ) | d x Calculation: Curves are given as follows f ( x ) = 2 x and g ( x ) = 6 − x We need to first calculate the intersection points of the curve. Equate the two functions, we get 2 x = 6 − x 2 x + x = 6 3 x = 6 x = 2 When x = 2 , y = 4 Thus, one intersection point is ( 2 , 4 ) . We need to calculate the area between vertical axis and ( 2 , 4 ) . Area between the curves is calculate as follows A = ∫ 0 2 | 2 x − ( 6 − x ) | d x A = ∫ 0 2 | 2 x − 6 + x | d x A = ∫ 0 2 | 3 x − 6 | d x Let us calculate the integral without the absolutes between the intervals [ 0 , 2 ]

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 6.3, Problem 26P

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Use the fundamental theorem to find the area between the curves f(x)=2x and g(x)=6−x from the vertical axis to their point of intersection.

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Chapter 6.3, Problem 25P

Chapter 6.3, Problem 27P

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Use the fundamental theorem to find the area between the curves f ( x ) = 2 x and g ( x ) = 6 − x from the vertical axis to their point of intersection.

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Use the fundamental theorem to find the area between the curves f(x)=2x and g(x)=6−x from the vertical axis to their point of intersection.

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Chapter 6 Solutions