/*! 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. 56 Use limits of definite integrals... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 56 (page 478)

Use limits of definite integrals to calculate each of the improper integrals in Exercises 21鈥�56.

鈭�2鈭�x-2x(x-1)dx

Short Answer

Expert verified

The integral is鈭�.

Step by step solution

01

Step 1. Given information.

The given integral is鈭�2鈭�x-2x(x-1)dx

02

Step 2. Value of the integral.

On simplifying,

鈭�x-2x(x-1)dx=鈭�-1x-1+2xdx=2ln(|x|)-ln(|x-1|)Now,鈭�2鈭�x-2x(x-1)dx=limB鈫�鈭�鈭�28x-2x(x-1)dx=lim8鈫�鈭�[2ln(|x|)-ln(|x-1|)]2B=limB鈫�鈭�[2ln(|B|)-ln(|B-1|)]-[2ln(|2|)-ln(|2-1|)]=鈭�

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

Solve the integral:鈭�3x+1secxdx

Which of the integrals that follow would be good candidates for trigonometric substitution? If a trigonometric substitution is a good strategy, name the substitution. If another method is a better strategy, explain that method.

(a)鈭�4+x2xdx (b)鈭�x4+x2dx

role="math" localid="1648759296940" (c)鈭�x24+x2dx (d)鈭�16鈭�x44+x2dx

Find three integrals in Exercises 21鈥�70 that we can anti-differentiate immediately after algebraic simplification.

Solve the integral :鈭�xex2+1dx

Find three integrals in Exercises 39鈥�74 that can be solved by using a trigonometric substitution of the form x=atanu.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

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.