Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Q 18. (page 451)

Describe strategy for solving the type of integral given.

∫secmxtannxdx,m odd andneven

Short Answer

Expert verified

Taketan2x=sec2x-1

Step by step solution

01

Step 1. Given information

Integral is∫secmxtannxdx

02

Step 2. Explanation

Consider the integral ∫secmxtannxdx

Usetan2x=sec2x-1

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!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve ∫x+2x2+4x32dxthe following two ways:

(a) with the substitution u=x2+4x;

(b) by completing the square and then applying the trigonometric substitution x + 2 = 2 sec u.

Explain why, if x=asecu, then a2sec2u−a2is −atanuif x<−aand is atanuif x>a. Your explanation should include a discussion of domains and absolute values.

Examples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.

(a) An integral with which we could reasonably apply trigonometric substitution with x=tan⁡u.

(b) An integral with which we could reasonably apply trigonometric substitution with x=4sec⁡u.

(c) An integral with which we could reasonably apply trigonometric substitution with x−2=3sin⁡u.

Explain why ∫2xx2+1dxand ∫1xlnxdxare essentially the same integral after a change of variables.

Complete the square for each quadratic in Exercises 28–33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.

2(x+2)2
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free