/*! 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. 69 Solve each of the definite integ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 69 (page 452)

Solve each of the definite integrals in Exercises 67鈥�76.

鈭�-蟺2蟺2cos3xdx

Short Answer

Expert verified

The solution of the integral is43.

Step by step solution

01

Step 1. Given Information

The given integral is鈭�-蟺2蟺2cos3xdx

02

Step 2. Rewrite and substitute

  • Use the trigonometric identities to rewrite the given integral.

鈭�-蟺2蟺2cos3xdx=鈭�-蟺2蟺21-sin2xcosxdx

  • Assume that sin(x)=u. So, cos(x)dx=du.
  • Substitute into the integral and change the limits accordingly.

鈭�-蟺2蟺21-sin2xcosxdx=鈭�sin-1-蟺2sin-1蟺21-u2du=鈭�-111-u2du

03

Step 3. Integrate

  • Integrate the obtained integral and substitute the limits to find the solution.

鈭�-111-u2du=鈭�-111du-鈭�-11u2du=u-u33-11=1-13+1-13=43

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)=sinx

What is a rational function? What does it mean for a rational function to be proper? Improper?

Solve the integral:鈭�3x+1secxdx

Solve鈭�x21+x2dx the following two ways:

(a) with the substitution u=tan-1x;

(b) with the trigonometric substitution x = tan u.

For each integral in Exercises 5鈥�8, write down three integrals that will have that form after a substitution of variables.

鈭�u2du
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Applied 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.