Chapter 5: Q 14. (page 451)

Describe strategy for solving the type of integral given.
$\int \sin^{m} x \cos^{n} x$ , one of $m, n$ odd

Short Answer

Expert verified

If $m$ is odd, write $\sin^{m} x = \sin x \sin^{m - 1} x$

If $n$ is odd, write $\cos^{n} x = \cos x \cos^{n - 1} x$

Step by step solution

Step 1. Given information

Integral is $\int \sin^{m} x \cos^{n} x d x$

Step 2. Explanation

Consider the integral $\int \sin^{m} x \cos^{n} x d x$

If $m$ is odd:

localid="1648898884043" $\sin^{m} x = \sin x \sin^{m - 1} x$

Write localid="1648898918126" $\sin^{2} x = 1 - \cos^{2} x$

Then let localid="1648898927779" $\cos x = u$

If $n$ is odd:

$\cos^{n} x = \cos x \cos^{n - 1} x$

Write width="119">cos2x=1-sin2x

Then let $\sin x = v$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Describe strategy for solving the type of integral given.
$\int \sin^{m} x \cos^{n} x$ , one of $m, n$ odd

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Pure Maths

Mechanics Maths

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Describe strategy for solving the type of integral given.∫sinmxcosnx, one of m,n odd

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Pure Maths

Mechanics Maths

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Describe strategy for solving the type of integral given.
$\int \sin^{m} x \cos^{n} x$ , one of $m, n$ odd