Explanation Given information: The provided curve is: y = x 2 − 2 x + 1 and y = x 2 − 5 x + 4 for x = 2 . Formula used: The area of the region bounded by equation y = f ( x ) and y = g ( x ) from x = a to x = b is given by A = ∫ a b [ f ( x ) − g ( x ) d x ] Here, f ( x ) and g ( x ) are continuous functions on [ a , b ] and if f ( x ) ≥ g ( x ) on [ a , b ] . \ Calculation: Consider the equation, y ( x ) = x 2 − 2 x + 1 Calculate the values y ( x ) at different values of x , Substitute x = 0 in the function y ( x ) = x 2 − 2 x + 1 . y ( 0 ) = ( 0 ) 2 − 2 ( 0 ) + 1 = 1 Substitute x = 1 in the function y ( x ) = x 2 − 2 x + 1 . y ( 1 ) = ( 1 ) 2 − 2 ( 1 ) + 1 = 0 Substitute x = 2 in the function y ( x ) = x 2 − 2 x + 1 . y ( 2 ) = ( 2 ) 2 − 2 ( 2 ) + 1 = 1 Substitute x = − 1 in the function y ( x ) = x 2 − 2 x + 1 . y ( − 1 ) = ( − 1 ) 2 − 2 ( − 1 ) + 1 = 4 The following table shows the different coordinate ( x , y ) for equation y ( x ) = x 2 − 2 x + 1 . x y ( x ) = x 2 − 2 x + 1 Coordinates ( x , y ) 0 1 ( 0 , 1 ) 1 0 ( 1 , 0 ) 2 1 ( 2 , 1 ) − 1 4 ( − 1 , 4 ) Now, consider y ( x ) = x 2 − 5 x + 4 Substitute x = 0 in the function y ( x ) = x 2 − 5 x + 4 . y ( 0 ) = ( 0 ) 2 − 5 ( 0 ) + 4 = 4 Substitute x = 1 in the function y ( x ) = x 2 − 5 x + 4 . y ( 0 ) = ( 1 ) 2 − 5 ( 1 ) + 4 = 0 Substitute x = 2 in the function y ( x ) = x 2 − 5 x + 4 . y ( 2 ) = ( 2 ) 2 − 5 ( 2 ) + 4 = − 2 Substitute x = − 1 in the function y ( x ) = x 2 − 5 x + 4

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 13.3, Problem 16E

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To calculate: The area of the region between y=x2−2x+1 and y=x2−5x+4 for x=2.

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Chapter 13.3, Problem 15E

Chapter 13.3, Problem 17E

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Chapter 13 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 13.1 - CHECKPOINT 1. For the interval [0, 2]. determine...Ch. 13.1 - Prob. 2CP Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E

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The area of the region between y = x 2 − 2 x + 1 and y = x 2 − 5 x + 4 for x = 2 .

Solution Summary: The author calculates the area of the region bounded by equations y=f(x) and

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To calculate: The area of the region between y=x2−2x+1 and y=x2−5x+4 for x=2.

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Chapter 13 Solutions