Explanation Given: F ' ( x ) = f ( x ) F ( 0 ) = 3 F ( 2 ) = 7 Formula Used: A r e a = ∫ a b f ( x ) d x , [ a , b ] = F ( b ) − F ( a ) Calculation: (a) The area under y = f ( x ) over [ 0 , 2 ] , f ( x ) ≥ 0 is ∫ 0 2 f ( x ) d x ∫ 0 2

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Riemann Sum

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Question

Chapter 5.4, Problem 1PQ

To determine

(a) The area under $y = f (x)$ over $[0, 2]$ if $f (x) \geq 0$

(b) The graphical representation of $F (2) - F (0)$ if $f (x)$ takes on both positive and negative values.

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See solution

Chapter 5.3, Problem 88E

Chapter 5.4, Problem 2PQ

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Chapter 5 Solutions

Calculus - Standalone book

Ch. 5.1 - Prob. 1PQ Ch. 5.1 - Prob. 2PQ Ch. 5.1 - Prob. 3PQ Ch. 5.1 - Prob. 4PQ Ch. 5.1 - Prob. 5PQ Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E

Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - 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(a) The area under y = f ( x ) over [ 0 , 2 ] if f ( x ) ≥ 0 (b) The graphical representation of F ( 2 ) − F ( 0 ) if f ( x ) takes on both positive and negative values.

Solution Summary: The author calculates the area under y = f ( x ) over [ 0, 2 ] if he takes both positive and negative values.

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(a) The area under $y = f (x)$ over $[0, 2]$ if $f (x) \geq 0$

(b) The graphical representation of $F (2) - F (0)$ if $f (x)$ takes on both positive and negative values.

Want to see the full answer?

Chapter 5 Solutions

(a) The area under y = f ( x ) over [ 0 , 2 ] if f ( x ) ≥ 0 (b) The graphical representation of F ( 2 ) − F ( 0 ) if f ( x ) takes on both positive and negative values.

Solution Summary: The author calculates the area under y = f ( x ) over [ 0, 2 ] if he takes both positive and negative values.

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(a) The area under y=f(x)over [0,2]if f(x)≥0 (b) The graphical representation of F(2)−F(0)if f(x)takes on both positive and negative values.

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Chapter 5 Solutions

(a) The area under $y = f (x)$ over $[0, 2]$ if $f (x) \geq 0$

(b) The graphical representation of $F (2) - F (0)$ if $f (x)$ takes on both positive and negative values.