/*! 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. 88 We can extend the technique of t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 88 (page 465)

We can extend the technique of trigonometric substitution to the hyperbolic functions. Use Theorem 2.20 and the identity cosh2x-sinh2x=1to solve each integral in Exercises 87鈥� 90 with an appropriate hyperbolic substitution x=asinhuorx=acoshu. (These exercises involve hyperbolic functions.)

鈭�12x2-3dx

Short Answer

Expert verified

The value of the integral is22cosh-16x3+C.

Step by step solution

01

Step 1. Given information.

The given integral is鈭�12x2-3dx.

02

Step 2. Substitution.

Now, Let x=62cosh(u)

Then,

x=62cosh(u)dx=62sinh(u)du

Since cosh2(u)-1=sinh2(u),

12x2-3=13cosh2(u)-3=33cosh2(u)-1=33sinh2(u)=33sinh(u)

03

Step 3. Value of the integral.

Now, we can write,

鈭�12x2-3dx=鈭�22du=22u=22cosh-16x3+C

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�x2exdx

Solve the integral:鈭�lnxdx

Solve the integral:鈭�lnx3dx.

Suppose v(x) is a function of x. Explain why the integral

of dv is equal to v (up to a constant).

Solve each of the integrals in Exercises 39鈥�74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.

鈭�x2+9x32dx
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

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.