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 (a) the Midpoint Rule and (b) Simpson's Rule to approximate the given integral with the specified value of $ n $. (Round your answers to six decimal places.) Compare your results to the actual value to determine the error in each approximation.
$ \displaystyle \int_0^\pi x cos x\ 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 Yuou Sun
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
Calculus 2 / BC
Chapter 7
Techniques of Integration
Section 7
Approximate Integration
Integration Techniques
Missouri State University
Oregon State University
Harvey Mudd College
University of Nottingham
Lectures
01:53
In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.
27:53
In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.
15:45
Use (a) the Midpoint Rule …
02:01
10:05
15:22
21:31
00:36
Use (a) the Trapezoidal Ru…
19:10
14:10
03:41
12:29
08:29
Okay, Problem sakes. You need a calculator to calculate this. First you need to catch this guy, Isaac. Go to minus two. And And if you go too far so you decided the intro into four pieces. Uh, this is or pie. This is tour pie. This is Bye. This is pie, right? And if you want to calculate an a mystical toe, the tirade. Ah, this point just this point at this point. But that that seems, uh, into all the leads up into Roy's by over or after a calculation, because find a and it's equal to minus 1.94544 uh, s what he's asked, the tax is pi minus zero, divided by four. So his pi work for and at zero is zero x four is hi eggs. That's one is ah, power for an X three is high over three times pi over four, right? Just technically everything. And you can get acts. It's equal to one minus 1.9 a 56 I Why? What as era e m is people toe I minus on this calculate, right? Ah, yes. He's got to go. I minus. That's that's all
View More Answers From This Book
Find Another Textbook