/*! 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. 52 For each pair of functions f,g聽... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q. 52 (page 386)

For each pair of functions f,gand interval localid="1648726145718" [a,b]in Exercises 41鈥�52, use definite integrals and the Fundamental Theorem of Calculus to find the exact area of the region between the graphs of f and g fromx=atox=b

f(x)=3x-2,g(x)=6-x,[a,b]=[3,7]

Short Answer

Expert verified

The exact area is2.237.

Step by step solution

01

Step 1. Given Information.

The given function and interval isf(x)=3x-2,g(x)=6-x,[a,b]=[3,7].

02

Step 2. Graph of the function.

The graph of the functions is,

03

Step 3. Required area.

The exact area will be,

鈭�37|f(x)-g(x)|dx=鈭�35(g(x)-f(x))dx+鈭�57(f(x)-g(x))dx=鈭�356-x-3x-2dx+鈭�573x-2-6+xdx=-x22+6x-3ln(x-2)35+3ln(x-2)+x22-6x57=-3ln(3)+4-3ln(3)+3ln(5)鈮�2.237

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

Approximate the area between the graph f(x)=x2and the x-axis from x=0 to x=4 by using four rectangles include the picture of the rectangle you are using

Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: tanx=sinxcosx).

鈭�2xlnx-xlnx2dx.

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.

鈭�鈭�32鈥�x2+52xdx

Verify that鈭�cotxdx=ln(sinx)+C. (Do not try to solve the integral from scratch.)

Calculate the exact value of each definite integral in Exercises 47鈥�52 by using properties of definite integrals and the formulas in Theorem 4.13.

鈭�04(2x-3)2+5dx
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Decision 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.