Explanation Given Information: The provided expression and the equations are ∫ R ∫ d A , y = x + 6 and y = x 2 respectively. Formula used: To determine the area in the plane by double integrals mostly two kind of strips are used. 1. Vertical strip: In case of vertical strip shown below the region bounded is given by, a ≤ x ≤ b g 1 ( x ) ≤ y ≤ g 2 ( x ) And the area of the region is given by, ∫ a b ∫ g 1 ( x ) g 2 ( x ) d y d x 2. Horizontal strip: In case of horizontal strip shown below the region bounded is given by, c ≤ y ≤ d h 1 ( y ) ≤ y ≤ h 2 ( y ) And the area of the region is given by, ∫ c d ∫ h 1 ( y ) h 2 ( y ) d x d y Calculation: Consider the expression ∫ R ∫ d A . First sketch the graph of region R which is bounded by the equations y = x + 6 and y = x 2 . The graph of the equation y = x 2 would be a parabola. For equation y = x + 6 , put different values of x in the equation to obtain different values of y in order to plot graph of the equation. For x = 0 , y = x + 6 = 0 + 6 = 6 For x = 1 y = x + 6 = 1 + 6 = 7 For x = 2 y = x + 6 = 2 + 6 = 8 For x = 3 y = x + 6 = 3 + 6 = 9 Now, construct a table showing different values of x and y as, x y = x + 6 0 6 1 7 2 8 3 9 Thus the graph of the equation y = x + 6 would be a straight line

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Question

Chapter 7.8, Problem 45E

To determine

To calculate: The area denoted by the expression ∫R∫dA where R is the region bounded by the equations y=x+6 and y=x2 using double integral.

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Chapter 7.8, Problem 44E

Chapter 7.8, Problem 46E

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Calculus: An Applied Approach (MindTap Course List)

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The graphs show the constraint...Ch. 7.6 - Prob. 45E Ch. 7.7 - Prob. 1CP Ch. 7.7 - Prob. 2CP Ch. 7.7 - Prob. 3CP Ch. 7.7 - Prob. 1SWU Ch. 7.7 - Prob. 2SWU Ch. 7.7 - Prob. 3SWU Ch. 7.7 - Prob. 4SWU Ch. 7.7 - Prob. 5SWU Ch. 7.7 - Prob. 6SWU Ch. 7.7 - Prob. 7SWU Ch. 7.7 - Prob. 8SWU Ch. 7.7 - Prob. 1E Ch. 7.7 - Prob. 2E Ch. 7.7 - Prob. 3E Ch. 7.7 - Prob. 4E Ch. 7.7 - Prob. 5E Ch. 7.7 - Prob. 6E Ch. 7.7 - Prob. 7E Ch. 7.7 - Prob. 8E Ch. 7.7 - Prob. 9E Ch. 7.7 - Prob. 10E Ch. 7.7 - Prob. 11E Ch. 7.7 - Prob. 12E Ch. 7.7 - Prob. 13E Ch. 7.7 - Prob. 14E Ch. 7.7 - Prob. 15E Ch. 7.7 - Demand A hardware retailer wants to know the...Ch. 7.7 - Prob. 17E Ch. 7.7 - HOW DO YOU SEE IT? 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Prob. 19E Ch. 7.9 - Prob. 20E Ch. 7.9 - Prob. 21E Ch. 7.9 - Prob. 22E Ch. 7.9 - Prob. 23E Ch. 7.9 - Prob. 24E Ch. 7.9 - Prob. 25E Ch. 7.9 - Population Density The population density (in...Ch. 7.9 - Prob. 27E Ch. 7.9 - Prob. 28E Ch. 7.9 - Prob. 29E Ch. 7.9 - Prob. 30E Ch. 7.9 - Average Weekly Profit A firms weekly profit P (in...Ch. 7.9 - Prob. 32E Ch. 7.9 - Prob. 33E Ch. 7.9 - Prob. 34E Ch. 7.9 - Prob. 35E Ch. 7.9 - Prob. 36E Ch. 7 - Plotting Points in Space In Exercises 1 and 2,...Ch. 7 - Prob. 2RE Ch. 7 - Prob. 3RE Ch. 7 - Prob. 4RE Ch. 7 - Prob. 5RE Ch. 7 - Prob. 6RE Ch. 7 - Prob. 7RE Ch. 7 - Prob. 8RE Ch. 7 - Prob. 9RE Ch. 7 - Prob. 10RE Ch. 7 - Prob. 11RE Ch. 7 - Prob. 12RE Ch. 7 - Finding a Trace of a Sphere In Exercises 13 and...Ch. 7 - Prob. 14RE Ch. 7 - Prob. 15RE Ch. 7 - Prob. 16RE Ch. 7 - Prob. 17RE Ch. 7 - Prob. 18RE Ch. 7 - Prob. 19RE Ch. 7 - Prob. 20RE Ch. 7 - Prob. 21RE Ch. 7 - Prob. 22RE Ch. 7 - Prob. 23RE Ch. 7 - Prob. 24RE Ch. 7 - Prob. 25RE Ch. 7 - Prob. 26RE Ch. 7 - 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Prob. 80RE Ch. 7 - Prob. 81RE Ch. 7 - Prob. 82RE Ch. 7 - Prob. 83RE Ch. 7 - Prob. 84RE Ch. 7 - Prob. 85RE Ch. 7 - Prob. 86RE Ch. 7 - Evaluating a Double Integral In Exercises 85-88,...Ch. 7 - Prob. 88RE Ch. 7 - Prob. 89RE Ch. 7 - Prob. 90RE Ch. 7 - Finding Area with a Double Integral In Exercises...Ch. 7 - Finding Area with a Double Integral In Exercises...Ch. 7 - Finding the Volume of a Solid Region In Exercises...Ch. 7 - Prob. 94RE Ch. 7 - Prob. 95RE Ch. 7 - Prob. 96RE Ch. 7 - Prob. 97RE Ch. 7 - Prob. 98RE Ch. 7 - Prob. 99RE Ch. 7 - Prob. 100RE Ch. 7 - Prob. 101RE Ch. 7 - Average Revenue A company sells two products whose...Ch. 7 - Prob. 103RE Ch. 7 - Average Production Repeat Exercise 103 for the...Ch. 7 - Prob. 1TYS Ch. 7 - Prob. 2TYS Ch. 7 - Prob. 3TYS Ch. 7 - Prob. 4TYS Ch. 7 - Prob. 5TYS Ch. 7 - Prob. 6TYS Ch. 7 - Prob. 7TYS Ch. 7 - Prob. 8TYS Ch. 7 - Prob. 9TYS Ch. 7 - Prob. 10TYS Ch. 7 - Prob. 11TYS Ch. 7 - Prob. 12TYS Ch. 7 - Prob. 13TYS Ch. 7 - Prob. 14TYS Ch. 7 - Prob. 15TYS Ch. 7 - 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The area denoted by the expression ∫ R ∫ d A where R is the region bounded by the equations y = x + 6 and y = x 2 using double integral.

Solution Summary: The author explains the formula used to determine the area in the plane by double integrals.

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To calculate: The area denoted by the expression ∫R∫dA where R is the region bounded by the equations y=x+6 and y=x2 using double integral.

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