/*! 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. 18 For each pair of definite integr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 18 (page 510)

For each pair of definite integrals in Exercises 13鈥�18, decide which, if either, is larger, without computing any integrals.

蟺鈭�04ydyand蟺鈭�48(8-y)dy

Short Answer

Expert verified

The value of both the integrals are equal.

Step by step solution

01

Step 1. Given Information

The given integrals are蟺鈭�04ydyand蟺鈭�48(8-y)dy

02

Step 2. Explanation

The integrals are of the form 蟺鈭�ab(f(y))2dywhich represents the volume of the solid formed by rotating the region bound by f(y)and y-axis in the interval[a,b]around x-axis.

On comparing the given integrals with the above given relation and observed that the function involved are f(y)=yintheinterval[0,4]andf(y)=8-yintheinterval[4,8]

Now, we will plot the graph of both the functions and identify the regions between the interval.

From the graph, we can say that both the regions are identical and symmetrical. This means the volume of the solids formed by rotating these regions will be equal. Thus, the value of both the integrals is also equal.

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

Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.

dydx=3x+1xy

Find the exact value of the arc length of each function f (x) on [a, b] by writing the arc length as a definite integral and then solving that integral .

fx=2x32+1,1,3

The centroid of the region between the graph of f(x) = x 2

and the x-axis on [0, 2].

The arc length of the curve is traced out by the graph of f(x)=ln(csxx)on the interval 蟺4,蟺2.

Explain how equality dydxxk,yk=螖yk螖xis relevant to Euler鈥檚 method.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Geometry

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.