/*! 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. 25 Use geometry (i.e., areas of tri... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q. 25 (page 352)

Use geometry (i.e., areas of triangles, rectangles, and circles) to find the exact values of each of the definite integrals in Exercises 21-28.

鈭�-111-x2dx.

Short Answer

Expert verified

The exact value of鈭�-111-x2dxis,蟺2.

Step by step solution

01

Step 1. Given information

鈭�-111-x2dx.

02

Step 2. The following figure shows the graph of 1-x2.

03

Step 3. Find the area.

The shaded region can be considered to be a half circle or radius1 unit.

The area of the shaded half circle is,

蟺谤22=蟺122=蟺2

Therefore, the exact value is,蟺2.

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

Your calculator should be able to approximate the area between a graph and the x-axis. Determine how to do this on your particular calculator, and then, in Exercises 21鈥�26, use the method to approximate the signed area between the graph of each function f and the x-axis on the given interval [a, b].

f(x)=1-2x,[a,b]=[-3,1]

Suppose f is a function whose average value on

[-2,5]is 10and whose average rate of change on

the same interval is -3. Sketch a possible graph for f .

Illustrate the average value and the average rate of change

on your graph of f.

For each function f and interval [a, b] in Exercises 27鈥�33, use the given approximation method to approximate the signed area between the graph of f and the x-axis on [a, b]. Determine whether each of your approximations is likely to be an over-approximation or an under-approximation of the actual area.

f(x)=x2,[a,b]=[0,3]left sum with

a) n = 3 b) n = 6

Suppose f is positive on (鈭掆垶, 鈭�1] and [2,鈭�) and negative on the interval [鈭�1, 2]. Write (a) the signed area and (b) the absolute area between the graph of f and the x-axis on [鈭�3, 4] in terms of definite integrals that do not involve absolute values.

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

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Pure 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.