Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Use the Midpoint Rule with the given value of $ n $ to approximate the integral. Round the answer to four decimal places.

$ \displaystyle \int^2_0 \frac{x}{x + 1}\, dx $, $ n = 5 $

0.9071

00:55

Amrita B.

03:07

Robert D.

Calculus 1 / AB

Chapter 5

Integrals

Section 2

The Definite Integral

Integration

Campbell University

Oregon State University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

03:50

Use the Midpoint Rule with…

00:43

01:10

03:01

03:20

00:19

01:41

$11-14=$ Use the Midpoint …

01:53

03:41

Use (a) the Trapezoidal Ru…

01:54

Yeah. So in the problem you see here, problem number 11, we have a definite integral and were asked to estimate this using uh rebound sums and rectangles, with the number of rectangles being five. So a crude approximation. So over the interval from 0 to 2, So two divided by five, his point four. So when I divide this up, you're going to have 0.4. Yeah 0.8 1.2, 1.6. Now were also asked to use the midpoint rule. So for mid points, the mid points are going to be a point to 0.6. Um 1.0, 1.4 and 1.8. So this integral From 0 to 2 of X over X plus one dx can be approximated by The areas of these rectangles. So each rectangle is a width .4, so 0.4 times. And now we have to figure out so it's going to be substituting each of these mid points into this formula. So it's going to be 0.2 over um actually just gonna be 1.2. So let me just do it that way, one plus 10.2, so point to over 1.2 Plus .6 over 1.6 plus one over to Plus 1.4 Over 2.4 plus 1.8 Over 2.8. So that is going to be my area approximation, so I can just do all of that on my calculator. So it is .4 times. And so we had what .4 divided about 1.4 Plus .8, divided by 1.8 plus um one divided by two, so one half Plus 1.4 Over 2.4 plus 1.8, divided by 2.8 98254 is approximation, so 98254 is my approximation. Yeah. And we can see how accurate that is. We'll find better ways of doing it ourselves. But I mean what if we were to ask for? Yeah. The integral From 0 to 2 of X over X plus one, So .90139. So I'm in the ballpark, but not a great approximation.

View More Answers From This Book

Find Another Textbook

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Use the Midpoint Rule with the given value of $ n $ to approximate the integ…

Use the Midpoint Rule with the given value of n toapproximate the integr…

$11-14=$ Use the Midpoint Rule with the given value of $n$ to approximate th…

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's …

02:07

If $ x^2 + xy + y^3 = 1, $ find the value of $ y" $ at the point where …

00:28

The velocity graph of a car accelerating from rest to a speed of 120 km/h ov…

00:04

(a) Find an approximation to the integral $ \displaystyle \int^4_0 (x^2 - 3x…

00:25

Find $ f'(x). $ Check that your answer is reasonable by comparing the g…

01:29

If a rock is thrown vertically upward from the surface of Mars with velocity…

01:04

Newton's Law of Gravitation says that the magnitude $ F $ of the force …

01:47

(a) Find the intervals of increase or decrease.(b) Find the local maximu…

07:41

(a) Estimate the area under the graph of $ f(x) = 1/x $ from $ x = 1 $ to $ …

02:42

Estimate the intervals of concavity to one decimal place by using a computer…

02:18

(a) Where does the normal line to the ellipse $ x^2 - xy + y^2 = 3 $ at the …

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.