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Math
CalculusCalculus (MindTap Course List)8th Edition

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Chapter 7.2, Problem 2E
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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
BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Evaluate the integral.

∫ sin 3 θ   cos 4 θ   d θ

To determine

To evaluate: The trigonometric integral ∫sin3θcos4θdθ

Explanation

Trigonometric integral of the form ∫sinmxcosnxdx can be solved using strategies depending on whether m and n are odd or even.

Formula used:

When power of sine in the integral is odd, save one sine factor and use the identity sin2x=1−cos2x to rewrite other terms in cosine function form:

∫sin2k+1xcosnxdx=∫cosnx(1−cos2x)ksinxdx

Then, use the substitution u=cosx

Given:

The integral, ∫sin3θcos4θdθ.

Calculation:

Rewrite the given integral in terms of cosine, saving one sine term:

∫sin3θcos4θdθ=∫sin2θcos4θsinθdθ

Use the identity sin2x+cos2x=1, to convert remaining terms into cosine:

∫sin2θcos4θsinθdθ=∫(1−cos2θ)cos4θsinθdθ

Use the substitution u=cosθ and du=−sinθdθ

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College Algebra (MindTap Course List)

A researcher has a sample of 30 rats that are all cloned from the same source. The 30 rats are genetically iden...

Research Methods for the Behavioral Sciences (MindTap Course List)

Explain the advantages and disadvantages of using random assignment as a method to prevent individual differenc...

Research Methods for the Behavioral Sciences (MindTap Course List)

Develop a compound interest model that represents the population of San Francisco. Use the information in Exerc...

Mathematics: A Practical Odyssey

A manufacturer is considering purchasing parts from three different suppliers. The parts received from the supp...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

The random variable x is known to be uniformly distributed between 1.0 and 1.5. a. Show the graph of the probab...

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

In many countries, grains and cereals arc the primary food source. The authors of the article Mineral Contents ...

Introduction To Statistics And Data Analysis

Solve each of the following equations using the multiplication principle of equality. Check each answer. C14=0

Mathematics For Machine Technology

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