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^{\pi}_0 x \sin^2x\, dx $, $ n = 4 $
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Bobby Barnes
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
00:35
Frank Lin
00:47
Amrita Bhasin
Calculus 1 / AB
Chapter 5
Integrals
Section 2
The Definite Integral
Integration
Elman R.
March 27, 2022
Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. ???? 2x sin2(x) dx, 0 n = 4
Missouri State University
Oregon State University
University of Nottingham
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.
03:20
Use the Midpoint Rule with…
0:00
Shown below.
01:17
00:17
03:07
02:40
01:42
03:50
01:09
00:43
so everyone used the midpoint formula to approximate this. Um, what I first do is just figure out what Dell Texas. So over here we have the formula for that. So r B is pi r a zero and that our in is going to be four. Or at least let Chuck Yeah, in this for So there's just gonna give us pie fourth. So now there's two ways to do. Says we're doing the midpoint formula. Um, we could just kind of use like the equation that I have a top here or what I normally like to do is first create like the set of partitions, like we would be doing the left or right. Riemann sums and then just average them. So I'm going to do that. So it's going to start from zero and then remember to get the next X I. We just had Delta X two. It would be pie, fourth pie, half three, pie fourth and then pie. And so now, So this is just a set of partitioning, and then the ones for the mid point we just average thes, so the average of that would be pie eight to the next one will be three pie eight five Pi eight and then seven Pi aids. All right. And so now if we want So since Delta X is just gonna be pi for you just kind of pull that out front of this So it would be pie fourth times that we would just plug in pi a three pilots and so on. So high eights times sine squared of high plus three I ate signed square of three pie eight and then plus five pi eights plus plus sine squared of five high eighth and then plus seven pi eight sine squared of seven pi tight. Right Then we just need to plug this song into a calculator and then get our estimate. So let me see what we get. So it's like approximately so pi fourth times, uh, 3.141 592 And then just gotta keep on going that we would need to multiply this by pie and then divide by four. And then this would be approximately 2.467 Or and I believe they wanted it to go to four decimal places. So this will be approximately integral from zero to pi of x times sine square of X x
View More Answers From This Book
Find Another Textbook
Campbell University
University of Michigan - Ann Arbor
Boston College
01:11
principal 65000,rate 9.5%p.a,time 7/2 years ..find the compound interest wit…
01:33
Write the basic unit of speed. If a car travels 216 km in 4 hours, calculate…
03:02
in how much time will rs. 10000 yield an interest of rs. 8500 at the rate of…
01:08
CASE STUDY :- In cartesian plane, image of the point (x, y) lying in the fir…
01:05
The result of adding 15 to x and dividing the answer by 4 is the same as tak…
00:29
b) A ream of paper ( 500 sheets of paper ) costs of Rs. 200. How much does a…
An electrician bought an old washing machine for rs.5000 he repaired it and …
01:07
Find the equation the line passing through (0,0) and making equal angles wit…
the centroid of the find the centroid of the triangle whose vertices are - …
Express 0.34 ( bar on 4 ) in the form p/q where p and q not equal to zero