Explanation Given information: The given functions are, f ( x ) = x , g ( x ) = 2 Concept used: If f ( x ) and g ( x ) are integrable functions, then the area between the graphs of f and g from x = a to x = b is ∫ a b | f ( x ) − g ( x ) | d x Calculation: Consider the given pair of functions: f ( x ) = x , g ( x ) = 2 Construct the area bounded by the region as shown: From the following figure, the area of the region between the graphs of f ( x ) and g ( x ) on the interval [ − 4 , 4 ] can be calculated as shown: ∫ − 4 4 | f ( x ) − g ( x ) | d x = ∫ − 4 − 3 ( f ( x ) − g ( x ) ) d x + ∫ − 3 − 2 ( f ( x ) − g ( x ) ) d x + ∫ − 2 − 1 ( f ( x ) − g ( x ) ) d x + ∫ − 1 0 ( f ( x ) − g ( x ) ) d x + ∫ 0 1 ( f ( x ) − g ( x ) ) d x + ∫ 1 2 ( f ( x ) − g ( x ) ) d x + ∫ 2 3 ( f ( x ) − g ( x ) ) d x + ∫ 3 4 ( f ( x ) − g ( x ) ) d x On further simplification ∫ 0

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Question

Chapter 4.6, Problem 39S

To determine

To approximate: the area of the region between the graphs of the given functions on the interval [−4,4] .

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Chapter 4.6, Problem 38S

Chapter 4.6, Problem 40S

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Chapter 4 Solutions

Calculus

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To approximate: the area of the region between the graphs of the given functions on the interval [ − 4 , 4 ] .

Solution Summary: The author calculates the approximated area of the region between the graphs of f(x) and

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To approximate: the area of the region between the graphs of the given functions on the interval [−4,4] .

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Chapter 4 Solutions