Explanation Given: The function f ( x ) = x 4 + x and g ( x ) = 1 + x . Theorem used: If f and g are continuous and f ( x ) ≥ g ( x ) over the interval [ a , b ] , then the area bounded by y = f ( x ) and y = g ( x ) for a ≤ x ≤ b is given exactly by A = ∫ a b [ f ( x ) − g ( x ) ] d x . Calculation: The functions are f ( x ) = x 4 + x and g ( x ) = 1 + x . Using online graphing calculator to sketch the graph of the functions f ( x ) = x 4 + x and g ( x ) = 1 + x is as shown in the below Figure 1. From Figure 1, it is observed that the functions f ( x ) and g ( x ) intersect at the points ( 0.83 , 1.83 ) and ( − 3.49 , 2.49 ) . The function f ( x ) is greater than g ( x ) in the interval [ − 3.49 , 0.83 ] . By the above mentioned theorem, the area of the shaded region is computed as follows, A = ∫ − 3

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

13th Edition

ISBN: 9780321869838

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen

Publisher: PEARSON

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Chapter 6.4, Problem 67E

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To find: The area bounded by the graphs of the equation f(x)=x4+x and g(x)=1+x.

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Chapter 6.4, Problem 66E

Chapter 6.4, Problem 68E

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Chapter 6 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

Ch. 6.1 - Matched Problem 1 Find the area bounded by f(x) =...Ch. 6.1 - Matched Problem 2 Find the area between the graph...Ch. 6.1 - Prob. 3MP Ch. 6.1 - Matched Problem 4Find the area bounded by f(x) =6 ...Ch. 6.1 - Matched Problem 5Find the area bounded by f(x)=2x2...Ch. 6.1 - Matched Problem 6Find the area (to three decimal...Ch. 6.1 - Prob. 7MP Ch. 6.1 - Prob. 1ED Ch. 6.1 - In Problems 18, use geometric formulas to find the...Ch. 6.1 - In Problems 18, use geometric formulas to find the...

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The area bounded by the graphs of the equation f ( x ) = x 4 + x and g ( x ) = 1 + x .

Solution Summary: The area of the shaded region is 5.47 square units.

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To find: The area bounded by the graphs of the equation f(x)=x4+x and g(x)=1+x.

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Chapter 6 Solutions