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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 8.5, Problem 56E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding the Area of a Region In Exercises 53-56, sketch the region bounded by the graphs of the functions and find the area of the region.

y = sec 2 x 4 , y = 4 − x 2 , x = − 1 , x = 1

To determine

To graph: The area bounded by the graph of y=sec2x4 and y=4−x2 for x=−1 to x=1.

Explanation

Given Information:

The provided functions are y=sec2x4 and y=4−x2 for x=−1 to x=1.

Formula used:

Write the formula of definite integral of ∫absec2udu.

∫absec2nudu=[tannun]ab

Here, n is the any number.

Write the formula of definite integral of ∫absinudu.

∫abundu=[un+1n+1]ab

Write the formula of definite integral of ∫abdu.

∫abdu=[u]ab

Graph:

Draw area bounded by graph of y=sec2x4 and y=4−x2 for x=−1 to x=1.

Consider provided function.

y=sec2x4

At x=−1,

yx=−1=sec2(−14)=1.065

At x=0,

yx=0=sec2(04)=sec20=1

At x=1,

yx=1=sec2(14)=1.065

Now, the table for ordered pair (x,y) for the function y=sec2x4 is shown below:

xy−11.0650111.065

Again, consider provided function.

y=4−x2

At x=−1,

yx=−1=4−(−1)2=3

At x=0,

yx=0=4−(0)2=4

At x=1,

yx=1=4−(1)2=3

Now, the table for ordered pair (x,y) for the function y=4−x2 is shown below:

xy−130413

Thus, the resulting graph of y=sec2x4 and y=4−x2 for x=−1 to x=1 is,

Calculation:

From above graph, the area bounded by the graph of y=sec2x4 and y=4−x2 for x=−1 to x=1 can be calculated as,

∫−11[(4−x2)−(sec2x4)]dx=2∫01[(4−x2)−(sec2x4)]dx

Rewrite

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Sect-8.1 P-1CPSect-8.1 P-2CPSect-8.1 P-3CPSect-8.1 P-4CPSect-8.1 P-1SWUSect-8.1 P-2SWUSect-8.1 P-3SWUSect-8.1 P-4SWUSect-8.1 P-5SWUSect-8.1 P-6SWU
Sect-8.1 P-7SWUSect-8.1 P-8SWUSect-8.1 P-9SWUSect-8.1 P-10SWUSect-8.1 P-1ESect-8.1 P-2ESect-8.1 P-3ESect-8.1 P-4ESect-8.1 P-5ESect-8.1 P-6ESect-8.1 P-7ESect-8.1 P-8ESect-8.1 P-9ESect-8.1 P-10ESect-8.1 P-11ESect-8.1 P-12ESect-8.1 P-13ESect-8.1 P-14ESect-8.1 P-15ESect-8.1 P-16ESect-8.1 P-17ESect-8.1 P-18ESect-8.1 P-19ESect-8.1 P-20ESect-8.1 P-21ESect-8.1 P-22ESect-8.1 P-23ESect-8.1 P-24ESect-8.1 P-25ESect-8.1 P-26ESect-8.1 P-27ESect-8.1 P-28ESect-8.1 P-29ESect-8.1 P-30ESect-8.1 P-31ESect-8.1 P-32ESect-8.1 P-33ESect-8.1 P-34ESect-8.1 P-35ESect-8.1 P-36ESect-8.1 P-37ESect-8.1 P-38ESect-8.1 P-39ESect-8.1 P-40ESect-8.1 P-41ESect-8.1 P-42ESect-8.1 P-43ESect-8.1 P-44ESect-8.1 P-45ESect-8.1 P-46ESect-8.1 P-47ESect-8.1 P-48ESect-8.1 P-49ESect-8.1 P-50ESect-8.1 P-51ESect-8.1 P-52ESect-8.1 P-53ESect-8.1 P-54ESect-8.1 P-55ESect-8.1 P-56ESect-8.1 P-57ESect-8.1 P-58ESect-8.2 P-1CPSect-8.2 P-2CPSect-8.2 P-3CPSect-8.2 P-4CPSect-8.2 P-5CPSect-8.2 P-6CPSect-8.2 P-7CPSect-8.2 P-1SWUSect-8.2 P-2SWUSect-8.2 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Elementary Geometry For College Students, 7e

True or False Label each of the following statements as either true or false. 12. The mutually disjoint cycles...

Elements Of Modern Algebra

Evaluate each expression without using a calculator, and write your answers in radians. arctan(33)

Trigonometry (MindTap Course List)

Finding a Limit In Exercises 41-46, write a simpler function that agrees with the given function at all but one...

Calculus of a Single Variable

Finding a Limit In Exercises 11-32, find the limit (if it exists). If it does not exist, explain why. limxcotx

Calculus: Early Transcendental Functions (MindTap Course List)

Use Herons Formula, A=s(sa)(sb)(sc), to find the exact area of a triangle that has lengths of sides 4 cm, 13 cm...

Elementary Geometry for College Students

RETIREMENT FUNDS Five and a half years ago, Chris invested 10,000 in a retirement fund that grew at the rate of...

Finite Mathematics for the Managerial, Life, and Social Sciences

Using Vectors to Determine Collinear Points In Exerciser 67-70, use vectors to determine whether the points are...

Calculus (MindTap Course List)

Study Guide for Stewart's Multivariable Calculus, 8th

The appropriate option for the value of (123).

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

Evaluating a Line Integral of a Vector Field Using Technology In Exercises 35 and 36, use a computer algebra sy...

Multivariable Calculus

Using the Definition of Limit In Exercises 45-56, find the limit L. Then use the definition to prove that the...

Calculus

Define a pre-post design and identify examples of this research design when it appears in a research report.

Research Methods for the Behavioral Sciences (MindTap Course List)

In Exercises 1-10, find the cardinal numbers of the set in each given pair to determine whether the sets are eq...

Mathematics: A Practical Odyssey

A social science researcher would like to determine the characteristics of people who live and work in small to...

Research Methods for the Behavioral Sciences (MindTap Course List)

Use the graph to identify any local maxima and local minima.

College Algebra (MindTap Course List)

As part of a study to determine the effects of allowing the use of credit cards for alcohol purchases in Canada...

Introduction To Statistics And Data Analysis

The Food Marketing Institute shows that 17% of households spend more than 100 per week on groceries. Assume the...

Statistics for Business & Economics, Revised (MindTap Course List)

In exercise 1, the following estimated regression equation based on 10 observations was presented. = 29.1270 +...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Express the following decimal degrees as degrees and minutes. When necessary, round the answer to the nearest w...

Mathematics For Machine Technology

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