/*! 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. 11 Riemann sums: Calculate the foll... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q. 11 (page 404)

Riemann sums: Calculate the following Riemann sum

approximations for the definite integral of f on [a, b], using the

given value of n .

The upper sum for fx=4x-x2on localid="1648811623340" 0,3,n=3

Short Answer

Expert verified

The sum is 10 .

Step by step solution

01

Step 1. Given information .

Consider the given functionfx=4x-x2on0,3.

02

Step 2. Formula used .

The Riemann sum formula for upper sum isUP,f=鈭�r=03Mr未xr.

03

Step 3. Find the value .

Divide open interval 0,3in three sub intervals 0,1,1,2,2,3where M is 1 , 2 , 3 substitute the value of M in the given function to find M1,M2,M3.

M1=4x-x2=4路1-1=3

M2=4,M3=3

Further simplify .

未x1=1-0=1未x2=2-1=1未x3=3-2=1

Substitute the values of M and 未xin the given formula .

UP,f=鈭�r=03Mr未xr=M1未x1+M2未x2+M3未x3=3脳1+4脳1+3脳1=10

M1=4x-x2=4脳1-1=3

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

Write each expression in Exercises 41鈥�43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).

3鈭�k=225k2+2鈭�kk=224-鈭�k=0251

Sum and constant-multiple rules: State the sum and constant-multiple rules for (a) derivatives and (b) limits.

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

鈭�24鈥�3e2x鈭�4dx

Given formula for the areas of each of the following geometric figures

a) area of circle with radius r

b) a semicircle of radius r

c) a right triangle with legs of lengths a and b

d) a triangle with base b and altitude h

e) a rectangle with sides of lengths w and l

f) a trapezoid with width w and heighth1,h2

Suppose f is a function whose average value on [-3,1] is

-2 and whose average rate of change on the same in-

terval is 4. Sketch a possible graph for f . Illustrate the

average value and the average rate of change on your

graph of f .
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

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.