Explanation 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 given functions are y = x and y = − x 3 . Use online graphing calculator to sketch the graph of the functions y = x and y = − x 3 in the interval [ − 2 , 2 ] is as shown below in Figure 1. From Figure 1, it is observed that the function y = x is greater than y = − x 3 in the interval [ 0 , 2 ] and the function y = x is lesser than y = − x 3 in the interval [ − 2 , 0 ] . By the above mentioned theorem, the area of the shaded region is computed as follows. A = ∫ 0 2 ( x − ( − x 3 ) ) d x + ∫ − 2 0 ( − x 3 − x ) <

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134668574

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

Publisher: PEARSON

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Chapter 6, Problem 15RE

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To find: The area bounded by the graphs of the equation y=x and y=−x3 over the interval −2≤x≤2.

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Chapter 6, Problem 14RE

Chapter 6, Problem 16RE

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Chapter 6 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th 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. 8MP Ch. 6.1 - Prob. 1ED 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 y = x and y = − x 3 over the interval − 2 ≤ x ≤ 2 .

Solution Summary: The area bounded by the graphs of the equation y=x is 12 square units.

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To find: The area bounded by the graphs of the equation y=x and y=−x3 over the interval −2≤x≤2.

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Chapter 6 Solutions