Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Use a power series to approximate the definite integral to six decimal places.$ \int^{0.3}_0 \frac {x}{1 + x^3} dx $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

0.044522

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 9

Representations of Functions as Power Series

Sequences

Series

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

01:59

In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence of real numbers is called a finite series. The sum of an infinite sequence of real numbers may or may not have a well-defined sum, and may or may not be equal to the limit of the sequence, if it exists. The study of the sums of infinite sequences is a major area in mathematics known as analysis.

02:28

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first "n" natural numbers (for a finite sequence). A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.

02:57

Use a power series to appr…

03:34

04:27

use a power Siri's to absolute mate. The definite in girl to six decimal places. All right, so Okay, well, first expand is to his power serious. And then Bruce Inmate, the baton in the world to six decimal places. Okay, so is it because? And they were from zero two zero one three in six times, Monets wanted our in extra or three in and from zero to infinity. Yes, And this is Uncle Chu. Okay, we can change Thie order of some and the Negro, and it becomes in the Girl of X to the three. M plus one, the eggs. So this is equal to of Missouri Divinity once went off in, sir, Ask me X to the power through in plus two o three, plus two. And from zero to zero point three. All right, so, yeah, we can only take the term. Let's say if he goes to Well, well, zero. So it's gonna be X to the power of two. So is X square over too have elsewhere. And in this one, it's become too. It becomes tio minus. Okay, so we plug in and Nikos one, it's extra power five oh, or five in, Plus hire older term, which is too small, which is too small for this difference, so can only calculate the first tutor. So it's gonna be half of square miners. One fifth Time's s for five. So minus zero, the plugging actually cost zero point three and this is equal Tio so half of zero point zero nine minus one fifty times. So, thereupon three times times, they're gonna authority. Power flow is equals to three times Tintin to power minus one to our five, which goes to Syria's syrup on zero for five months we're going to comes, so it's gonna be two. Thirty four to thirty to forty three times ten to the power of Amon. It's fine, and we can use a calculator to simply buy it. And the result? It's going to be just a moment says they're one to comes two, forty three times. So ten to horror oneness for syrup on zero zero zero zero one. Yeah, and the result is Okay, so it says to six decimal places. All right, so the realist syrup on zero four four five one four. Okay, that is thie approximation of the definite, definite integral to six decimal places.

View More Answers From This Book

Find Another Textbook

Numerade Educator

02:18

'This table presents the price distribution of shoe styles offered by a…

02:16

'Find the following quantity if v = 3i - 4j + 2k and w = - 2i + 3j - 3k…

01:26

'18 1og3 63 - log3 3'

05:51

'12.3 [Xrl2-03] How effective are antilock brakes (ABS)? These brakes…

00:22

"then the slope o/ this line isIf the equation for the regression l…

01:43

'10. Heather is collecting dimes. She saves one dime on the first day; …

'3- What is the best order to form the product ABCD if A,B, C,and D are…

01:40

'3.24 Suppose we measure the noise in a resistor (with no applied volta…

01:51

'Solve the equation: Igx = 2 -Ig25+2lg3 2'