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Math
CalculusCalculus (MindTap Course List)8th Edition

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Chapter 7.2, Problem 60E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Use a graph of the integrated to guess the value of the integral. Then use the methods of this section to prove that your guess is correct.

∫ 0 2 sin 2 π x   cos 5 π x   d x

To determine

To evaluate:

the value of integral from the graph of the integrand and then perform the integration to verify.

Explanation

Trigonometric integral of the form ∫sinmxcosnxdx can be solved using the identity for sinAcosA.

Given:

∫02sin2πxcos5πxdx.

Formula used:

The identity sinAcosB=12[sin(A−B)+sin(A+B)].

Calculation:

The graph of integrand from x=0 to 2 is as shown below:

Notice from the graph that the shape of the curve from x=0 to 1 is repeated for x=1 to 2, but inverted about the x-axis. Hence for each bell shapes above the x-axis, there exists an equal bell shape below the x-axis. So, the total area above x-axis under the graph is equal to the area under the graph below the x-axis. Hence, the integral from 0 to 2 will be zero. Now, perform the integration and confirm is it evaluates to zero.

Use the identity sinAcosB=12[sin(A−B)+sin(A+B)] with A as 2πx and B as 5πx:

∫02sin2πxcos5πxdx=12∫02(sin(2πx−5πx)+sin(2πx+5πx))dx=

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Finite Mathematics for the Managerial, Life, and Social Sciences

In Review Exercises 18 to 23, use construction methods with the accompanying figure. Given: ABC Find: The incen...

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Finding a Particular Solution Using Separation of Variables In Exercises 19-28, find the particular solution of...

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Equivalent Vectors In Bunches 5-8, find the vector: u and v whose initial and terminal points are given. Show t...

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Checking Points in a Plane In Exercises 37 and 38, determine whether each point lies in the plane. x+2y4z1=0 (a...

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Identify the three modalities of measurement and explain the strengths and weaknesses of each.

Research Methods for the Behavioral Sciences (MindTap Course List)

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

A library has five copies of a certain textbook on reserve of which two copies (1 and 2) are hardcover books an...

Introduction To Statistics And Data Analysis

Determine the answers to the following exercises which are based on corresponding parts. Identify the angle tha...

Mathematics For Machine Technology

The prior probabilities for events A1, A2, and A3 are P(A1) = .20, P(A2) = .50, and P(A3) = .30. The conditiona...

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Describe, compare, and contrast the five research strategies (descriptive, correlational, experimental, quasi-e...

Research Methods for the Behavioral Sciences (MindTap Course List)

Practice: Determine how many zeros each polynomial function has. P(x)=32x111x51

College Algebra (MindTap Course List)

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