/*! 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. 12 Riemann sums: Calculate each of ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q. 12 (page 404)

Riemann sums: Calculate each of the following Riemann sum

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

given value of n.

The lower sum for fx=4x-x2on 0,3,n=6.

Short Answer

Expert verified

The lower sum is 5 .

Step by step solution

01

Step 1. Given information .

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

02

Step 2. Formula used .

Riemann sum formula for lower sum isLP,f=鈭�r=03mr未xr.

03

Step 3. Find the lower sum for fx=4x-x2 on 0,3 .

Divide the no in open interval from zero to 3 in 6 sub interval to find 未x

and m . The sub intervals are 0,1,1,2,2,3,3,4,4,5,5,6.

The value of m1=0,m2=1,m3=2,m4=3,m5=4,m6=5

Put the values of m in given function fx=4x-x2. we get fx=4x-x2=4脳0-0=0=m1

m2=3,m3=4,m4=3,m5=0,m6=-5

Substitute the values in formula LP,f=鈭�r=03mr未xr

where 未xis 1.

鈬�m1未x1+m2未x2+m3未x3+m4未x4+m5未x5+m6未x6鈬�0脳1+3脳1+4脳1+3脳1+0脳1+-5脳1鈬�0+3+4+3+0-5鈬�5

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

Explain why at this point we don鈥檛 have an integration formula for the functionf(x)=secx whereas we do have an integration formula for f(x)=sinx.

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

鈭�蟺/4蟺/2鈥�csc鈦�xcot鈦�xdx

Determine which of the limit of sums in Exercises 47鈥�52 are infinite and which are finite. For each limit of sums that is finite, compute its value

limn鈫�鈭�鈭�k=1n(k2+k+1)

Determine which of the limit of sums in Exercises 47鈥�52 are infinite and which are finite. For each limit of sums that is finite, compute its value

limn鈫�鈭�鈭�k=1n1+kn2.1n

Find the sum or quantity without completely expanding or calculating any sums.

Given鈭�k=310ak=12and鈭�k=210ak=23, finda2.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Calculus

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.