/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 32 Use limits of definite integrals... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 32 (page 478)

Use limits of definite integrals to calculate each of the improper integrals in Exercises.

鈭�1鈭�x+1x2dx

Short Answer

Expert verified

The improper integral 鈭�1鈭�x+1x2dxdiverges.

Step by step solution

01

Step 1. Given information. 

The given integral is the following.

鈭�1鈭�x+1x2dx

02

Step 2. Value of integral. 

Consider functionf(x)=x+1x2

localid="1648879879677" f(x)=x+1x2=xx2+1x2=1x+1x21x+1x2>1x2

In the interval [1,鈭�)we have localid="1648879786507" x+1x2>1x2.

As we know that localid="1648884171467" 鈭�1鈭�1x2dxis converse and integral of functions less than 1x2will be converse.

But x+1x2鈮�1x2so it cannot be converse.

so1x+1x2is diverse.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

For each function u(x) in Exercises 9鈥�12, write the differential du in terms of the differential dx.

u(x)=1x

Find three integrals in Exercises 27鈥�70 for which a good strategy is to use integration by parts with u=xand dv the remaining part.

Solve given integrals by using polynomial long division to rewrite the integrand. This is one way that you can sometimes avoid using trigonometric substitution; moreover, sometimes it works when trigonometric substitution does not apply.

鈭�x3-3x2+2x-3x2+1dx

Give an example of an integral for which trigonometric substitution is possible but an easier method is available. Then give an example of an integral that we still don鈥檛 know how to solve given the techniques we know at this point.

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

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

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.