BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

Using the Midpoint Rule In Exercises 7-14, use the Midpoint Rule with n =   5 to approximate the area of the region bounded by the graph of f and the x-axis over the interval. Sketch the region. See Examples 2 and 3.

Function Interval

f ( x ) = 4 x 2   [ 1 , 0 ]

To determine

To calculate: The area bounded by the function f(x)=4x2 and x axis over the interval [1,0] by mid-point rule. Also graph the area of the respective region.

Explanation

Given Information:

The provided function is f(x)=4x2 area of this function is calculated on the interval [1,0] and the provided interval will be divided into 5 sub interval as n=5.

Formula used:

The approximate area of any definite integral baf(x)dx by the use of midpoint rule is calculated by the use of following steps.

Step1: First divide the provided interval of the function into n sub intervals by the use of formula;

Δx=ban where [a,b] are the intervals and n is the subinterval value and Δx is the width.

Step2: Use above subinterval find the midpoint of each sub interval.

Step3: Final step is to obtain approximate area by calculating function f at each mid-point from the use of formula;

abf(x)dxban[f(x1)+f(x2)+f(x3)+....+f(xn)].

Calculation:

Consider the provided function f(x)=4x2.

Now, put n=5, a=1 and b=0 to find the width of subinterval as;

Δx=0(1)5=15

Width Δx of the provided interval will be 15.

So, the interval [1,0] with width 15 will be divided into 5 subintervals as;

[1,45],[45,35],[35,25],[25,15],[15,0].

Now, the value of midpoint of each sub interval is calculated as;

[x1,x2]=x1+x22 where x1,x2 are the upper value and lower value of the sub-interval

So, for subinterval [1,45] mid-point is;

[1+45]2=0.9

Similarly, for subinterval [45,35] mid-point is;

[45+35]2=0.7

For subinterval [35,25] mid-point is;

[35+25]2=0

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started
Sect-5.1 P-3SWUSect-5.1 P-4SWUSect-5.1 P-5SWUSect-5.1 P-6SWUSect-5.1 P-7SWUSect-5.1 P-8SWUSect-5.1 P-9SWUSect-5.1 P-10SWUSect-5.1 P-1ESect-5.1 P-2ESect-5.1 P-3ESect-5.1 P-4ESect-5.1 P-5ESect-5.1 P-6ESect-5.1 P-7ESect-5.1 P-8ESect-5.1 P-9ESect-5.1 P-10ESect-5.1 P-11ESect-5.1 P-12ESect-5.1 P-13ESect-5.1 P-14ESect-5.1 P-15ESect-5.1 P-16ESect-5.1 P-17ESect-5.1 P-18ESect-5.1 P-19ESect-5.1 P-20ESect-5.1 P-21ESect-5.1 P-22ESect-5.1 P-23ESect-5.1 P-24ESect-5.1 P-25ESect-5.1 P-26ESect-5.1 P-27ESect-5.1 P-28ESect-5.1 P-29ESect-5.1 P-30ESect-5.1 P-31ESect-5.1 P-32ESect-5.1 P-33ESect-5.1 P-34ESect-5.1 P-35ESect-5.1 P-36ESect-5.1 P-37ESect-5.1 P-38ESect-5.1 P-39ESect-5.1 P-40ESect-5.1 P-41ESect-5.1 P-42ESect-5.1 P-43ESect-5.1 P-44ESect-5.1 P-45ESect-5.1 P-46ESect-5.1 P-47ESect-5.1 P-48ESect-5.1 P-49ESect-5.1 P-50ESect-5.1 P-51ESect-5.1 P-52ESect-5.1 P-53ESect-5.1 P-54ESect-5.1 P-55ESect-5.1 P-56ESect-5.1 P-57ESect-5.1 P-58ESect-5.1 P-59ESect-5.1 P-60ESect-5.1 P-61ESect-5.1 P-62ESect-5.1 P-63ESect-5.1 P-64ESect-5.1 P-65ESect-5.1 P-66ESect-5.1 P-67ESect-5.1 P-68ESect-5.1 P-69ESect-5.1 P-70ESect-5.1 P-71ESect-5.1 P-72ESect-5.1 P-73ESect-5.1 P-74ESect-5.1 P-75ESect-5.2 P-1CPSect-5.2 P-2CPSect-5.2 P-3CPSect-5.2 P-4CPSect-5.2 P-5CPSect-5.2 P-6CPSect-5.2 P-7CPSect-5.2 P-8CPSect-5.2 P-1SWUSect-5.2 P-2SWUSect-5.2 P-3SWUSect-5.2 P-4SWUSect-5.2 P-5SWUSect-5.2 P-6SWUSect-5.2 P-7SWUSect-5.2 P-8SWUSect-5.2 P-9SWUSect-5.2 P-1ESect-5.2 P-2ESect-5.2 P-3ESect-5.2 P-4ESect-5.2 P-5ESect-5.2 P-6ESect-5.2 P-7ESect-5.2 P-8ESect-5.2 P-9ESect-5.2 P-10ESect-5.2 P-11ESect-5.2 P-12ESect-5.2 P-13ESect-5.2 P-14ESect-5.2 P-15ESect-5.2 P-16ESect-5.2 P-17ESect-5.2 P-18ESect-5.2 P-19ESect-5.2 P-20ESect-5.2 P-21ESect-5.2 P-22ESect-5.2 P-23ESect-5.2 P-24ESect-5.2 P-25ESect-5.2 P-26ESect-5.2 P-27ESect-5.2 P-28ESect-5.2 P-29ESect-5.2 P-30ESect-5.2 P-31ESect-5.2 P-32ESect-5.2 P-33ESect-5.2 P-34ESect-5.2 P-35ESect-5.2 P-36ESect-5.2 P-37ESect-5.2 P-38ESect-5.2 P-39ESect-5.2 P-40ESect-5.2 P-41ESect-5.2 P-42ESect-5.2 P-43ESect-5.2 P-44ESect-5.2 P-45ESect-5.2 P-46ESect-5.2 P-47ESect-5.2 P-48ESect-5.2 P-49ESect-5.2 P-50ESect-5.2 P-51ESect-5.2 P-52ESect-5.2 P-53ESect-5.2 P-54ESect-5.2 P-55ESect-5.2 P-56ESect-5.2 P-57ESect-5.2 P-58ESect-5.2 P-59ESect-5.2 P-60ESect-5.2 P-61ESect-5.2 P-62ESect-5.3 P-1CPSect-5.3 P-2CPSect-5.3 P-3CPSect-5.3 P-4CPSect-5.3 P-5CPSect-5.3 P-6CPSect-5.3 P-7CPSect-5.3 P-1SWUSect-5.3 P-2SWUSect-5.3 P-3SWUSect-5.3 P-4SWUSect-5.3 P-5SWUSect-5.3 P-6SWUSect-5.3 P-7SWUSect-5.3 P-8SWUSect-5.3 P-1ESect-5.3 P-2ESect-5.3 P-3ESect-5.3 P-4ESect-5.3 P-5ESect-5.3 P-6ESect-5.3 P-7ESect-5.3 P-8ESect-5.3 P-9ESect-5.3 P-10ESect-5.3 P-11ESect-5.3 P-12ESect-5.3 P-13ESect-5.3 P-14ESect-5.3 P-15ESect-5.3 P-16ESect-5.3 P-17ESect-5.3 P-18ESect-5.3 P-19ESect-5.3 P-20ESect-5.3 P-21ESect-5.3 P-22ESect-5.3 P-23ESect-5.3 P-24ESect-5.3 P-25ESect-5.3 P-26ESect-5.3 P-27ESect-5.3 P-28ESect-5.3 P-29ESect-5.3 P-30ESect-5.3 P-31ESect-5.3 P-32ESect-5.3 P-33ESect-5.3 P-34ESect-5.3 P-35ESect-5.3 P-36ESect-5.3 P-37ESect-5.3 P-38ESect-5.3 P-39ESect-5.3 P-40ESect-5.3 P-41ESect-5.3 P-42ESect-5.3 P-43ESect-5.3 P-44ESect-5.3 P-45ESect-5.3 P-46ESect-5.3 P-47ESect-5.3 P-48ESect-5.3 P-49ESect-5.3 P-50ESect-5.3 P-51ESect-5.3 P-52ESect-5.3 P-53ESect-5.3 P-54ESect-5.3 P-55ESect-5.3 P-56ESect-5.3 P-57ESect-5.3 P-58ESect-5.3 P-1QYSect-5.3 P-2QYSect-5.3 P-3QYSect-5.3 P-4QYSect-5.3 P-5QYSect-5.3 P-6QYSect-5.3 P-7QYSect-5.3 P-8QYSect-5.3 P-9QYSect-5.3 P-10QYSect-5.3 P-11QYSect-5.3 P-12QYSect-5.3 P-13QYSect-5.3 P-14QYSect-5.3 P-15QYSect-5.3 P-16QYSect-5.3 P-17QYSect-5.3 P-18QYSect-5.3 P-19QYSect-5.3 P-20QYSect-5.3 P-21QYSect-5.4 P-1CPSect-5.4 P-2CPSect-5.4 P-3CPSect-5.4 P-4CPSect-5.4 P-5CPSect-5.4 P-6CPSect-5.4 P-7CPSect-5.4 P-8CPSect-5.4 P-9CPSect-5.4 P-1SWUSect-5.4 P-2SWUSect-5.4 P-3SWUSect-5.4 P-4SWUSect-5.4 P-5SWUSect-5.4 P-6SWUSect-5.4 P-7SWUSect-5.4 P-1ESect-5.4 P-2ESect-5.4 P-3ESect-5.4 P-4ESect-5.4 P-5ESect-5.4 P-6ESect-5.4 P-7ESect-5.4 P-8ESect-5.4 P-9ESect-5.4 P-10ESect-5.4 P-11ESect-5.4 P-12ESect-5.4 P-13ESect-5.4 P-14ESect-5.4 P-15ESect-5.4 P-16ESect-5.4 P-17ESect-5.4 P-18ESect-5.4 P-19ESect-5.4 P-20ESect-5.4 P-21ESect-5.4 P-22ESect-5.4 P-23ESect-5.4 P-24ESect-5.4 P-25ESect-5.4 P-26ESect-5.4 P-27ESect-5.4 P-28ESect-5.4 P-29ESect-5.4 P-30ESect-5.4 P-31ESect-5.4 P-32ESect-5.4 P-33ESect-5.4 P-34ESect-5.4 P-35ESect-5.4 P-36ESect-5.4 P-37ESect-5.4 P-38ESect-5.4 P-39ESect-5.4 P-40ESect-5.4 P-41ESect-5.4 P-42ESect-5.4 P-43ESect-5.4 P-44ESect-5.4 P-45ESect-5.4 P-46ESect-5.4 P-47ESect-5.4 P-48ESect-5.4 P-49ESect-5.4 P-50ESect-5.4 P-51ESect-5.4 P-52ESect-5.4 P-53ESect-5.4 P-54ESect-5.4 P-55ESect-5.4 P-56ESect-5.4 P-57ESect-5.4 P-58ESect-5.4 P-59ESect-5.4 P-60ESect-5.4 P-61ESect-5.4 P-62ESect-5.4 P-63ESect-5.4 P-64ESect-5.4 P-65ESect-5.4 P-66ESect-5.4 P-67ESect-5.4 P-68ESect-5.4 P-69ESect-5.4 P-70ESect-5.4 P-71ESect-5.4 P-72ESect-5.4 P-73ESect-5.4 P-74ESect-5.4 P-75ESect-5.4 P-76ESect-5.4 P-77ESect-5.4 P-78ESect-5.4 P-79ESect-5.5 P-1CPSect-5.5 P-2CPSect-5.5 P-3CPSect-5.5 P-4CPSect-5.5 P-5CPSect-5.5 P-6CPSect-5.5 P-1SWUSect-5.5 P-2SWUSect-5.5 P-3SWUSect-5.5 P-4SWUSect-5.5 P-5SWUSect-5.5 P-6SWUSect-5.5 P-7SWUSect-5.5 P-8SWUSect-5.5 P-1ESect-5.5 P-2ESect-5.5 P-3ESect-5.5 P-4ESect-5.5 P-5ESect-5.5 P-6ESect-5.5 P-7ESect-5.5 P-8ESect-5.5 P-9ESect-5.5 P-10ESect-5.5 P-11ESect-5.5 P-12ESect-5.5 P-13ESect-5.5 P-14ESect-5.5 P-15ESect-5.5 P-16ESect-5.5 P-17ESect-5.5 P-18ESect-5.5 P-19ESect-5.5 P-20ESect-5.5 P-21ESect-5.5 P-22ESect-5.5 P-23ESect-5.5 P-24ESect-5.5 P-25ESect-5.5 P-26ESect-5.5 P-27ESect-5.5 P-28ESect-5.5 P-29ESect-5.5 P-30ESect-5.5 P-31ESect-5.5 P-32ESect-5.5 P-33ESect-5.5 P-34ESect-5.5 P-35ESect-5.5 P-36ESect-5.5 P-37ESect-5.5 P-38ESect-5.5 P-39ESect-5.5 P-40ESect-5.5 P-41ESect-5.5 P-42ESect-5.5 P-43ESect-5.5 P-44ESect-5.5 P-45ESect-5.5 P-46ESect-5.5 P-47ESect-5.5 P-48ESect-5.5 P-49ESect-5.5 P-50ESect-5.5 P-51ESect-5.5 P-52ESect-5.5 P-53ESect-5.5 P-54ESect-5.5 P-55ESect-5.5 P-56ESect-5.5 P-57ESect-5.5 P-58ESect-5.6 P-1CPSect-5.6 P-2CPSect-5.6 P-3CPSect-5.6 P-1SWUSect-5.6 P-2SWUSect-5.6 P-3SWUSect-5.6 P-4SWUSect-5.6 P-5SWUSect-5.6 P-6SWUSect-5.6 P-7SWUSect-5.6 P-8SWUSect-5.6 P-9SWUSect-5.6 P-10SWUSect-5.6 P-1ESect-5.6 P-2ESect-5.6 P-3ESect-5.6 P-4ESect-5.6 P-5ESect-5.6 P-6ESect-5.6 P-7ESect-5.6 P-8ESect-5.6 P-9ESect-5.6 P-10ESect-5.6 P-11ESect-5.6 P-12ESect-5.6 P-13ESect-5.6 P-14ESect-5.6 P-15ESect-5.6 P-16ESect-5.6 P-17ESect-5.6 P-18ESect-5.6 P-19ESect-5.6 P-20ESect-5.6 P-29ESect-5.6 P-30ESect-5.6 P-31ESect-5.6 P-33ECh-5 P-1RECh-5 P-2RECh-5 P-3RECh-5 P-4RECh-5 P-5RECh-5 P-6RECh-5 P-7RECh-5 P-8RECh-5 P-9RECh-5 P-10RECh-5 P-11RECh-5 P-12RECh-5 P-13RECh-5 P-14RECh-5 P-15RECh-5 P-16RECh-5 P-17RECh-5 P-18RECh-5 P-19RECh-5 P-20RECh-5 P-21RECh-5 P-22RECh-5 P-23RECh-5 P-24RECh-5 P-25RECh-5 P-26RECh-5 P-27RECh-5 P-28RECh-5 P-29RECh-5 P-30RECh-5 P-31RECh-5 P-32RECh-5 P-33RECh-5 P-34RECh-5 P-35RECh-5 P-36RECh-5 P-37RECh-5 P-38RECh-5 P-39RECh-5 P-40RECh-5 P-41RECh-5 P-42RECh-5 P-43RECh-5 P-44RECh-5 P-45RECh-5 P-46RECh-5 P-47RECh-5 P-48RECh-5 P-49RECh-5 P-50RECh-5 P-51RECh-5 P-52RECh-5 P-53RECh-5 P-54RECh-5 P-55RECh-5 P-56RECh-5 P-57RECh-5 P-58RECh-5 P-59RECh-5 P-60RECh-5 P-61RECh-5 P-62RECh-5 P-63RECh-5 P-64RECh-5 P-65RECh-5 P-66RECh-5 P-67RECh-5 P-68RECh-5 P-69RECh-5 P-70RECh-5 P-71RECh-5 P-72RECh-5 P-73RECh-5 P-74RECh-5 P-75RECh-5 P-76RECh-5 P-77RECh-5 P-78RECh-5 P-79RECh-5 P-80RECh-5 P-81RECh-5 P-82RECh-5 P-83RECh-5 P-84RECh-5 P-85RECh-5 P-86RECh-5 P-87RECh-5 P-88RECh-5 P-89RECh-5 P-90RECh-5 P-91RECh-5 P-92RECh-5 P-93RECh-5 P-94RECh-5 P-95RECh-5 P-96RECh-5 P-97RECh-5 P-98RECh-5 P-99RECh-5 P-100RECh-5 P-101RECh-5 P-102RECh-5 P-103RECh-5 P-104RECh-5 P-105RECh-5 P-106RECh-5 P-107RECh-5 P-108RECh-5 P-109RECh-5 P-110RECh-5 P-111RECh-5 P-112RECh-5 P-113RECh-5 P-114RECh-5 P-115RECh-5 P-1TYSCh-5 P-2TYSCh-5 P-3TYSCh-5 P-4TYSCh-5 P-5TYSCh-5 P-6TYSCh-5 P-7TYSCh-5 P-8TYSCh-5 P-9TYSCh-5 P-10TYSCh-5 P-11TYSCh-5 P-12TYSCh-5 P-13TYSCh-5 P-14TYSCh-5 P-15TYSCh-5 P-16TYSCh-5 P-17TYSCh-5 P-18TYSCh-5 P-19TYSCh-5 P-20TYSCh-5 P-21TYSCh-5 P-22TYS

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Find an equation of the tangent line to the curve at the given point. y=1+x3,(2,3)

Single Variable Calculus: Early Transcendentals, Volume I

Solve the equations in Exercises 112 for x (mentally, if possible). x3=1

Finite Mathematics and Applied Calculus (MindTap Course List)

A sample of n = 9 scores has X = 108. What is the sample mean?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 13-20, sketch a set of coordinate axes and plot each point. 16. (3, 4)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Describe the scores in a sample that has standard deviation of zero.

Statistics for The Behavioral Sciences (MindTap Course List)

Solve each equation and check: x+3=4(57x)

Elementary Technical Mathematics

Name the four components of a mathematical system.

Elementary Geometry for College Students

For the area of the shaded region, which integral form, dx or dy, should be used? a) dx b) dy c) Either...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

True or False: div curl F = 0.

Study Guide for Stewart's Multivariable Calculus, 8th

Identify possible sources and use them to identify a topic area for research.

Research Methods for the Behavioral Sciences (MindTap Course List)

Find all real solutions of each equation. 16x+4=x+4

College Algebra (MindTap Course List)