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

(a) Find the approximations $T_{10}$ and $M_{10}$ for $\int_{1}^{2} e^{1 / x} d x$(b) Estimate the errors involved in the approximations ofpart (a).(c) How large do we have to choose $n$ so that the approxi-mations $T_{n}$ and $M_{n}$ to the integral in part (a) are accu-rate to within 0.0001$?$

a) $$2.0191 $$b) $$\approx 0.0034$$c) $$n=59$$

Calculus 2 / BC

Chapter 6

TECHNIQUES OF INTEGRATION

Section 5

Approximate Integration

Integration Techniques

Improper Integrals

Missouri State University

Oregon State University

Harvey Mudd College

Baylor University

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

05:14

(a) Find the approximation…

06:14

03:57

15:29

02:53

Compute the error bound fo…

02:35

Find the approximations $ …

02:19

13:52

Find the approximations $L…

20:22

Approximate the integral u…

11:15

Consider the integral $\in…

for ricin 18 6 20 using the rule or integration from one to do yeah to the power one over X, d X and in equals 10. Does the X the woods off interval with equal to minus 1/10? It will go, went one. Then we conclude the values at the interval. Boundaries for F X equal. Mhm, the power one over X and each X. We will find the value if it's at X equal one. Fix it going. Seven. Wow! And it's equal 1.1. It takes equal 2.48 at X equal. One way to fix equal 2.3 and etcetera still X equals two. If X would be equal 1.64 Hey! And we right out of the refrigerator rule for in the plasma at our condition. 11 terms and they feel in the numbers of from the table through de 10. With equal. There's the X for over to off the blind boy If exports plus who, if it's one lost to If the accessory etcetera, then to if it's night loss. If it's again by director institution, we will find the value off teeth and equal 2.2 19 76 Using the midpoint toe, we calculate the values at the mid points off each interval. At the checks, we will get the value off you're fixed, you will get the value of X equals 1.5 Sorry x equal Ongoing 05 to fix equal 2.59 at X equals 1.15 If a sequel don't work 38 at X equal one going to five if X equal, Don't worry total and etcetera till X equal 1.95 to fix equal one Brain 66 nine For the midpoint rule we multiplies of its off. Each interval tells the X Times is a some off each fx upon the midpoint table. So in with him it won the X off the Blind Boy if in one plus it's a me too glass, if a mystery plus, if in For Plus it's in my life, plus etcetera till a feminine so and within. With equal two point 09 102 for Section B, take the 1st and 2nd derivatives off FX because effort double dash X is decreasing on the interval, one to do. The maximum value occurs at the left. Interval pound 81 1. Yeah. This is the lower limit for King. So if slash x equal minus one over exist where the blind bite you is a power one over x the federal dash X equal toe over. Execute multiplied by It was a power one by not one over X plus one block plus three look dreary. Last one. So far X is about four multiplied. Boy e is about our one over X. By substitution, we find that if fallible dash at X equal to equal Oh, boy. 515 and the F at X equal one equal 8.154 And this is the value off K, Uschi A equal one and p equal to In the e t equations off. We will find 80 equal. Okay, but the blue eyed boy B minus a Yeah, que Well, what? Well, and Miss Squared my director institution. We'll find that it is smaller than sorry. He teach smaller than particularly Bob Wind Oh, 68 And using Kale equal one and be equal to in the e m equations off. So he am smaller than or equal key about the blind boy. B minus e que Well, What During 34 in the square. 24. Any square so e m. Smaller than or equal or going for 34 four section C If X equals e to the power one over X so if finish x equal A to the power one over X off the blind boy minus X to the barber minus two. If global Dash X will equal he to the power one over X multiplied by two x plus one over experts of our four F global dish is decreasing and more than 04 so the maximum is at X equal. One key equal, incurable dish for X equal one equal three e about it going 15 for eight. But since then, the Bozidar by said that trapezoidal error bound expression to smaller than or equal over a who won. So we will find that K multiplied. B minus A. You will, sir 12 in the square, smaller than or equal or going toe one. So ST e the blood boy to minus one. Q. Over the wealth in this world smaller than or equal who went Oh, go on. So e over four in the square. Smaller than what we're going toe one and so and with bigger them for equal. No. You for what went for for 44 About 82 wait for rounding up to the nearest integral. So in equal it is three bye said the midpoint. Error bound expression toe 2.1. So key applied by P minus Take you over 24 in the square. Well, smaller than equal. We're goingto one by directive institution. We will find that in the square. Well, bigger than e over eight multiplied boy. Oh, fun. And then and then will bigger them or equal 58.3 and rounding up to the nearest integral. So in we're equal 59.

View More Answers From This Book

Find Another Textbook

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

(a) Find the approximations $ T_{10} $ and $ M_{10} $ for $ \displaystyle \i…

(a) Find the approximations $ T_[10} $, $ M_{10} $, and $ S_{10} $ for $ \di…

(a) Find the approximations $ T_8 $ and $ M_8 $ for the integral $ \displays…

(a) Find the approximations $T_{8}$ and $M_{8}$ for the integral$\int_{0…

Compute the error bound for the approximations $T_{10}$ and $M_{10}$ to $\in…

Find the approximations $ L_n $, $ R_n $, $ T_n $, and $ M_n $ for $ n = 5 $…

Find the approximations $L_{n}, R_{n}, T_{n},$ and $M_{n}$ to the integral

Approximate the integral using (a) the midpoint approximation $M_{10},$ (b) …

Consider the integral $\int_{0}^{\pi} \sin x d x$

(a) Use a calculat…

05:08

Determine whether each integral is convergent or divergent. Evaluate those t…

01:08

If $x$ is measured in meters and $f(x)$ is measured in newtons,what are …

10:38

$7-34=$ Evaluate the integral.$$\int \frac{x^{2}-x+6}{x^{3}+3 x} d x$$

15:51

One method of slowing the growth of an insect populationwithout using pe…

06:10

$7-16=$ Use (a) the Trapezoidal Rule, (b) the Midpoint Rule,and (c) Simp…

03:30

$5-10=$ Sketch the region enclosed by the given curves. Decidewhether to…

02:22

Alabama Instruments Company has set up a production line to manufacture a ne…

01:00

Find the volume of the described solid $S .$A right circular cone with h…

02:28

Evaluate the integral.$\int \frac{x}{\sqrt{1+x^{2}}} d x$

01:04

$43-48=$ Find the general indefinite integral.$$\int(\sin x+\sinh x) d x…

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.