10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

Textbook Problem

Finding an Indefinite Integral In Exercises 21–36, find the indefinite integral.

∫ x 2 36 − x 2 d x

To determine

To calculate: The value of indefinite integral ∫x236−x2dx.

The provided integral is ∫x236−x2dx.

Formula used:

∫xndx=xn+1n+1+C

Trigonometric identity:

sin2θ+cos2θ=1sin2θ=1−2cosθ2sin2θ=2sinθcosθ

Integration of Cosine function is;

∫cosθdθ=sinθ+C

Calculation:

None of the basic integration rules apply here. Now to use the trigonometric substitution observe that 36−x2 is in the form of a2−u2.

Let x=6sinθ, then differentiate both sides with respect to x to get:

Now by using the figure find the value of θ,

sinθ=x6=perpendicularhypotenusebase=36−x2

The value of cosθ is;

cosθ=36−x26θ=arcsinx4

Substituting 6sinθ for x in the integral ∫x236−x2dx as;

∫x236−x2dx=∫36sin2θ36−(6sinθ)2⋅6cosθdθ=∫36sin2θ36−36sin2θ⋅6cosθdθ=∫36sin2θ36(1−sin2θ)⋅6cosθdθ

Recall the formula of trigonometric property, sin2θ+cos2θ=1

Apply the trigonometric property and simplify:

∫136−x2dx=36∫6sin2θcosθ36(1−sin2θ)dθ=36∫6sin2θcosθ16

Check out a sample textbook solution.

Chapter 8 Solutions

Additional Math Solutions

Single Variable Calculus

Calculus of a Single Variable

Finite Mathematics and Applied Calculus (MindTap Course List)

Single Variable Calculus: Early Transcendentals

Calculus: An Applied Approach (MindTap Course List)

Calculus: Early Transcendental Functions

Precalculus: Mathematics for Calculus (Standalone Book)

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

Calculus (MindTap Course List)

Calculus: Early Transcendentals

Multivariable Calculus

Single Variable Calculus: Early Transcendentals, Volume I

Applied Calculus

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

Intermediate Algebra

Understanding Basic Statistics

Elementary Technical Mathematics

Mathematical Applications for the Management, Life, and Social Sciences

Contemporary Mathematics for Business & Consumers

Elements Of Modern Algebra

Finite Mathematics

Mathematical Excursions (MindTap Course List)

Trigonometry (MindTap Course List)

Probability and Statistics for Engineering and the Sciences

Elementary Geometry For College Students, 7e

Statistics for The Behavioral Sciences (MindTap Course List)

Essentials Of Statistics

Calculus: Early Transcendental Functions (MindTap Course List)

Elementary Geometry for College Students

Finite Mathematics for the Managerial, Life, and Social Sciences

Calculus (MindTap Course List)

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

Multivariable Calculus

Study Guide for Stewart's Multivariable Calculus, 8th

Research Methods for the Behavioral Sciences (MindTap Course List)

Mathematics For Machine Technology

Mathematics: A Practical Odyssey

College Algebra (MindTap Course List)

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

Introduction To Statistics And Data Analysis

Research Methods for the Behavioral Sciences (MindTap Course List)

STATISTICS F/BUSINESS+ECONOMICS-TEXT

MathCalculusCalculus10th Edition

Calculus

Solutions

Calculus

Finding an Indefinite Integral In Exercises 21–36, find the indefinite integral. ∫ x 2 36 − x 2 d x

Still sussing out bartleby?

The Solution to Your Study Problems

Chapter 8 Solutions

Additional Math Solutions

Find more solutions based on key concepts

For the function h whose graph is given, state the value of each quantity, if it exists. If it does not exist, ...

Evaluating a Limit In Exercises 15-42, evaluate the limit, using LHpitals Rule if necessary. limxxx2+1

In Exercises 5-8, graph the given function or equation. f(x)=4xx2 with domain [0,4]

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. 20. 2+0.5...

Determining Continuity In Exercises 111122, describe the interval(s) on which the function is continuous. Expla...

Verifying a Parallelogram In Exercise 71 and 72, use vectors to show that the points form the vertices of a par...

Complete each statement and name the property of real numbers you have used. (a) ab = __________; __________ Pr...

In Exercises 39-54, simplify the expression. (Assume that x, y, r, s, and t are positive.) 43. x3/4x1/4

Assume that f is a one-to-one function. a If f(6)=17, what is f1=(17)? b If f1(3)=2, what is f(2)?

Use Property 11 to estimate the value of the integral. 60. Tsin4(x+y)dA, T is the triangle enclosed by the line...

Solve the boundary-value problem, if possible. 28. y" - 8y' + 17y = 0, y(0) = 3, y() = 2

Prove the identity. 43. sin(2+x)=cosx

Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Place the following scores in a frequency distribution table. Based on the frequencies, what is the shape of th...

For problems 15-26, simplify each numerical expression. Be sure to take advantage of the properties whenever th...

For Problems 9-19. please provide the following information. (a) What is the level of significance? State the n...

A laboratory technician records the life span (in months) of rats treated at birth with a fertility hormone. Fr...

What part of the real number line corresponds to the interval.

Raise the following fractions to higher terms as indicated. 15 to hundredths

Perform the computations in exercises and express the results in standard form .

By any method, determine all possible real solutions of each equation in Exercises 1330. Check your answers by ...

Use a difference table to predict the next term in the sequence 1,0,9,32,75,144,245,....

Prove that each of the following identities is true. csc1cot=cotcsc+1

A sample of n captured Pandemonium jet fighters results in serial numbers x1, x2, x3,..., xn. The CIA knows tha...

Show that the triangle whose vertices are A-2,-3, B4,5, and C-4,1 is a right triangle.

Find the mean, median, and mode for the scores in the following frequency distribution table: X F 6 5 2 4 2 3 2...

SOC/CJ A survey shows that 10 of the population is victimized by property crime each year. A random sample of 5...

Estimating a Limit Consider the function f(x)=(1+x)1/x Estimate limx0(1+x)1/x by evaluating f at x-values near ...

In Exercises 37 to 40, use induction to state a conclusion. Several movies directed by Lawrence Garrison have w...

COLLEGE ADMISSIONS Applicants who wish to be admitted to a certain professional school in a large university ar...

Graphical Reasoning In Exercises 41 and 42, consider the force field shown in the figure. Is the force field co...

What is the number of the integral formula in your texts Table of Integrals that may be used to evaluate dxx2x2...

ProofProve that an object moving in a straight line at a constant speed has an acceleration of 0.

By the method of variation of parameters, a particular solution to, where , and:

Describe the purpose of the descriptive research strategy, explain how it differs from the purpose of other res...

Determine 1.

Exercise 7-12, can be done as homework problem or in-class activities. Draw a graph with five vertices in which...

Practice Use the graph to determine each functions domain and range.

The national highway Traffic Safety administration reported the percentage of traffic accidents occurring each ...

The Wall Street Journal (February 15, 1972) reported that General Electric was sued in Texas for sex discrimina...

Although experiments typically manipulate some aspect of the environment to create different treatment conditio...

Do you think global warming will have an impact on you during your lifetime? A CBS News/New York times poll of ...

Math
Calculus Calculus 10th Edition

Finding an Indefinite Integral In Exercises 21–36, find the indefinite integral.

∫ x 2 36 − x 2 d x

Complete each statement and name the property of real numbers you have used. (a) ab = ; Pr...