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

Find the approximations $ T_n $, $ M_n $, and $ S_n $ for $ n = 6 $ and 12. Then compute the corresponding errors $ E_T $, $ E_M $, and $ E_S $. (Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.) What observations can you make? In particular, what happens to the errors when $ n $ is doubled?

$ \displaystyle \int_1^4 \frac{1}{\sqrt{x}}\ dx $

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

Campbell University

University of Nottingham

Idaho State University

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.

02:01

Find the approximations $ …

29:31

Find the approximations $T…

18:44

02:19

02:35

04:07

$27-28$ Find the approxima…

23:00

Find the approximations $L…

30:47

03:14

Okay problem 28 point: we need to find t: minus n is equal to second 12 and the corresponding errors begin to know, there's a corresponding errors and an estimate. You want to find the estimate errors. You can use this ominous, but if not you want to find a corresponding address. It'S just. I minus m r s r t right, so you need to find t m s. Here'S function p m and as just do it, you know everything you know. What f is- and you know, dirx just use the function to find p m as what happens to the errors taboo. You divided the whole interval into more pieces, so your approximation is more close to the real value, so the errors becomes smaller and if you want to know how to compute, i let me find out this 1 or square x, dx right. It is equal to x to the negative the x, so we want to find 2 times an take a derivative of this function. It becomes this function, so it is equal to this. 1 right is just a 2 times. 2. Minus 1 is just 2 point right. It'S just 2 and just compute all autocenes and compare with.

View More Answers From This Book

Find Another Textbook

04:26

The number of points,X, scored in a game has the probability distribution be…

10:00

(1 point) Consider the path r(t) (4t,2t2 , 2 ln t) defined for t > 0_ Fin…

03:32

2. (a) Sketch the curve by uSing parametric equations to plot points Indicat…

01:45

survey was given t0 random sample of 400 people living in = certain communit…

03:36

5.35 Cholesterol levels of teenagers. A study of the health of teenagers pla…

02:34

A machine at K&A Tube & Manufacturing Company produces copper tubing…

04:24

In the following probability distribution, the random variable X represents …

03:51

5. Let be non-constant, continuous function defined on a closed interval [a.…

01:35

Question 612 ptsIf | write the natural numbers like this:{1,2,3,…