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 2 − 6 x and y = 0 . Use online graphing calculator to sketch the graph of the functions y = x 2 − 6 x and y = 0 over the interval [ − 1 , 2 ] is as shown below in Figure 1. From Figure 1, it is observed that the function y = x 2 − 6 x is greater than y = 0 in the interval [ − 1 , 0 ] and the function y = x 2 − 6 x is lesser than y = 0 in the interval [ 0 , 2 ] . By the above mentioned theorem, the area of the shaded region is computed as follows. A = ∫ − 1 0 ( ( x 2 − 6 x ) − 0 ) d x + ∫ 0 2 ( 0 − ( x 2 − 6 x ) ) d x = ∫ − 1 0

14th Edition

ISBN: 9780134856667

Author: Stocker

Publisher: VST

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Question

Chapter 6.1, Problem 46E

To determine

To find: The area bounded by the graphs of the equation y=x2−6x and y=0 over the interval −1≤x≤2.

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Chapter 6.1, Problem 45E

Chapter 6.1, Problem 47E

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Chapter 6 Solutions

EBK CALCULUS FOR BUSINESS, ECONOMICS, L

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The area bounded by the graphs of the equation y = x 2 − 6 x and y = 0 over the interval − 1 ≤ x ≤ 2 .

Solution Summary: The area of the shaded region is 12.667 square units.

To find: The area bounded by the graphs of the equation y=x2−6x and y=0 over the interval −1≤x≤2.

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Chapter 6 Solutions