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Use series to approximate the definite integral to within the indicated accuracy.

$ \int^{1/2}_0 x^3 \arctan x dx $ $ \text { (four decimal places)} $

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Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Sequences

Series

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

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.

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Use series to approximate …

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The problem is, is Siri's to approximate is a happening bro too willing to indicated accuracy integral from zero to one half X Cube has attended the packs. So first, huh? Our candid in't. Thanks. It's the culture some from zero to infinity. Next one, too, in terms extra chewing one over. Sure so X Cube Agent axe. Physical to some hero between twenty if you want and how I axed you children, us or over here and integral from zero to one half excuse you have planned. Jax is equal to some from zero to twenty. If you want to end times, thanks to children. US off over shooting us. Want times Children from zero to French is a call to some from zero to infinity. Next to want any times one over shoot to kill us off. Chewing us one comes through us far. Half in is equal to three this term. One over. True to your love counts, eleven pounds is about zero point zero zero zero zero zero six. So we have They're Siri's is about one cover shoot five pounds off times one minus one country, two to seven seven pounds. Greed plus one over two to nine. It's nine comes off, which is about zero point. See your own cereal off

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