Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
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 $
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Robert Daugherty
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
00:30
Frank Lin
00:55
Amrita Bhasin
Calculus 1 / AB
Chapter 5
Integrals
Section 2
The Definite Integral
Integration
Missouri State University
Campbell University
Harvey Mudd College
Idaho State University
Lectures
05:53
In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.
40:35
In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.
03:50
Use the Midpoint Rule with…
06:15
00:43
02:40
01:09
03:01
03:20
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
01:35
The area of a square field is 169 sq . what will be its perimeter
01:47
The points A ( 1, 1 ), B ( 3, 2 ) and C ( 5,3 ) cannot be the vertices of th…
05:17
sum of first 4 terms of an A.S is 72 sum of first 9 terms is also 72.a) what…
06:27
AB and BC form a right angle at their point of intersection, B.If the co…
01:59
what is the area of a trapezium whose parallel sides are 12cm and 16cm whose…
03:14
Find k, if the line 3x + 4y + k = 0 touches 9x + 16y = 144.
01:02
Rakesh attended 3 client meetings on Monday, 6 client meetings and 1 interna…
04:57
Peter bought a cycle for 7000 and marked it at a price that ensures a profit…
01:15
if a÷b 5÷8then find the values of the following ratios b:a
01:17
verify whether on dividing polynomial x²-5x+3 by x-3 the reminder is zero or…