Explanation Given Information: The provided functions are y = x 2 and y = 4 x + 5 . Formula Used: The area between two graphs: If f ( x ) ≥ g ( x ) for all x in [ a , b ] (so that the graph of f doesn’t move below that of g ), then the area of the region between the graphs of f and g and between x = a and x = b is given by: A = ∫ a b [ f ( x ) − g ( x ) d x ] Calculation: The provided functions are y = x 2 and y = 4 x + 5 . The points can be obtained by keeping them equal: x 2 = 4 x + 5 x 2 − 4 x − 5 = 0 x 2 − 5 x + x − 5 = 0 x ( x − 5 ) + 1 ( x − 5 ) = 0 Further simplify, x ( x − 5 ) + 1 ( x − 5 ) = 0 ( x + 1 ) ( x − 5 ) = 0 Therefore, x = − 1 or x = 5 . Substitute x = − 1 in the equation y = x 2 . y = x 2 = ( − 1 ) 2 = 1 Now, substitute x = 5 in the equation y = x 2 . y = x 2 = ( 5 ) 2 = 25 Therefore, both graphs intersect at points ( − 1 , 1 ) and ( 5 , 25 ) . Consider the equation y = x 2 . The graph is obtained as follows: Substitute x = 0 in y = x 2 . y = ( 0 ) 2 = 0 Substitute x = 1 in y = x 2 . y = ( 1 ) 2 = 1 Substitute x = 3 in y = x 2 . y = ( 3 ) 2 = 9 Summarized all points in a table, x y (x,y) 0 0 ( 0 , 0 ) 1 1 ( 1 , 1 ) 3 9 ( 3 , 9 ) Now, consider the equation y = 4 x + 5 , Substitute x = 0 in y = 4 x + 5 . y = 4 ( 0 ) + 5 = 5 Substitute x = 1 in y = 4 x + 5 . y = 4 ( 1 ) + 5 = 9 Substitute x = 3 in y = 4 x + 5

12th Edition

ISBN: 9780357865095

Author: HARSHBARGER

Publisher: CENGAGE L

See similar textbooks

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Videos

Question

Chapter 13, Problem 20RE

To determine

To calculate: The area under the graph of y=x2 and y=4x+5 using the definite integral method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13, Problem 19RE

Chapter 13, Problem 21RE

Students have asked these similar questions

Microsoft Excel snapshot for random sampling: Also note the formula used for the last column 02 x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51)) A B 1 No. States 2 1 ALABAMA Rand No. 0.925957526 3 2 ALASKA 0.372999976 4 3 ARIZONA 0.941323044 5 4 ARKANSAS 0.071266381 Random Sample CALIFORNIA NORTH CAROLINA ARKANSAS WASHINGTON G7 Microsoft Excel snapshot for systematic sampling: xfx INDEX(SD52:50551, F7) A B E F G 1 No. States Rand No. Random Sample population 50 2 1 ALABAMA 0.5296685 NEW HAMPSHIRE sample 10 3 2 ALASKA 0.4493186 OKLAHOMA k 5 4 3 ARIZONA 0.707914 KANSAS 5 4 ARKANSAS 0.4831379 NORTH DAKOTA 6 5 CALIFORNIA 0.7277162 INDIANA Random Sample Sample Name 7 6 COLORADO 0.5865002 MISSISSIPPI 8 7:ONNECTICU 0.7640596 ILLINOIS 9 8 DELAWARE 0.5783029 MISSOURI 525 10 15 INDIANA MARYLAND COLORADO

The spread of an infectious disease is often modeled using the following autonomous differential equation: dI - - BI(N − I) − MI, dt where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of transmission, and μ is the rate at which people recover from infection. Close a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria. b) (5 points) For the equilbria in part a), determine whether each is stable or unstable. c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the dt function by hand.) Identify the equilibria as stable or unstable in the graph. d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.

Find the indefinite integral. Check Answer: 7x 4 + 1x dx

Chapter 13 Solutions

MATHEMATICAL APPLICATIONS FOR THE MGT

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

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The area under the graph of y = x 2 and y = 4 x + 5 using the definite integral method.

Solution Summary: The author calculates the area under the graph of y=x2 and = 4x+5 using the definite integral method.

Concept explainers

Videos

To calculate: The area under the graph of y=x2 and y=4x+5 using the definite integral method.

Want to see the full answer?

Chapter 13 Solutions