Explanation Given: The given functions are f ( x ) = 20 + x − x 2 g ( x ) = x 2 − 5 x Calculation: You have to find the area between two curves. If f ( x ) and g ( x ) are two functions in [ a , b ] such that f ( x ) ≥ g ( x ) the area between them is A = ∫ a b f ( x ) − g ( x ) d x The given functions are f ( x ) = 20 + x − x 2 g ( x ) = x 2 − 5 x The region between the graphs is shown by the area bounded by f ( x ) = 20 + x − x 2 , g ( x ) = x 2 − 5 x , x = 4 and x = 8 From graph it is clear that f ( x ) ≥ g ( x ) in [ 4 , 5 ] and g ( x ) ≥ f ( x ) in [ 5 , 8 ] Hence the integration can be split into two parts from [ 4 , 5 ] and [ 5 , 8 ] ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

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Question

Chapter 6.1, Problem 8E

To determine

Area of region enclosed by the graphs in $[4, 8]$

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Chapter 6.1, Problem 7E

Chapter 6.1, Problem 9E

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Chapter 6 Solutions

Calculus - Standalone book

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Area of region enclosed by the graphs in [ 4 , 8 ]

Solution Summary: The author explains that the area between two graphs is 262 3 square units, and the integration can be split into two parts.

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Area of region enclosed by the graphs in $[4, 8]$

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Area of region enclosed by the graphs in [ 4 , 8 ]

Solution Summary: The author explains that the area between two graphs is 262 3 square units, and the integration can be split into two parts.

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Area of region enclosed by the graphs in [4,8]

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Chapter 6 Solutions

Area of region enclosed by the graphs in $[4, 8]$