Riemann–Stieltjes integral: Difference between revisions

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m →‎References: WP:CHECKWIKI error fixes - Replaced special characters in sortkey using AWB (9095)
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Needs to explain why E[|f(X|] needs to be finite not just E[f(X)]
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[[File:Shell integration.svg|thumb|right|200px]]
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{{Calculus |Integral}}
 
'''Shell integration''' (the '''shell method''' in [[integral calculus]]) is a means of [[calculation|calculating]] the [[volume]] of a [[solid of revolution]], when integrating along an axis ''perpendicular to'' the axis of revolution. While less intuitive than [[disc integration]], it usually produces simpler integrals.
 
It makes use of the so-called "representative [[cylinder (geometry)|cylinder]]". Intuitively speaking, part of the [[graph of a function]] is rotated around an [[axis of rotation|axis]], and is modelled by an infinite number of hollow pipes, all infinitely thin.
 
The idea is that a "representative [[rectangle]]" (used in the most basic forms of [[integral|integration]] &ndash; such as ∫&nbsp;''x''&nbsp;''dx'') can be rotated about the [[solid of revolution|axis of revolution]]; thus generating a hollow cylinder. Integration, as an accumulative process, can then calculate the ''integrated'' volume of a "[[Family (disambiguation)#Mathematics|family]]" of shells (a shell being the outer edge of a hollow cylinder) &ndash; as volume is the [[antiderivative]] of area, if one can calculate the [[lateral surface]] area of a shell, one can then calculate its volume.
 
Shell integration can be considered a special case of evaluating a [[double integral]] in [[polar coordinates]].
 
== Calculation ==
 
Mathematically, this method is represented by:
 
if the rotation is around the [[y-axis]] (vertical axis of revolution) then,  
 
:<math>2\pi \int_{a}^{b} xh(x)\,dx</math>
 
 
else if the rotation is around the [[x-axis]] (horizontal axis of revolution) then,
 
:<math>2\pi \int_{a}^{b} yh(y)\,dy</math>
 
 
[[File:Shell-integration.png|thumb|center|200px]]
 
==See also==
*[[Solid of revolution]]
*[[Disk integration]]
*[[Radius]]
 
==References==
*[http://www.cliffsnotes.com/study_guide/topicArticleId-39909,articleId-39907.html CliffsNotes.com. Volumes of Solids of Revolution]. 12 Apr 2011.
*{{MathWorld|title=Method of Shells|urlname=MethodofShells}}
*Frank Ayres, Elliott Mendelson:''Schaum's outlines: Calculus''. McGraw-Hill Professional 2008, ISBN 978-0-07-150861-2. pp.&nbsp;244–248 ({{Google books|Ag26M8TII6oC|online copy|page=244}})
 
{{DEFAULTSORT:Shell Integration}}
[[Category:Integral calculus]]

Revision as of 16:06, 12 February 2014

When you were young, possibly we were 1 of those fortunate persons that didnt need weight loss help. Maybe you were chasing kids, working at an outside job, cooking, cleaning plus living an active lifestyle. Its not which men over 50 and post-menopausal ladies are not active. However frequently they are less active. This might be as a result of physical limitations, including arthritis, or because they have just gotten used to a more sedentary lifestyle in retirement or even if they are nonetheless functioning.

If almost all of the population is overweight (based on the bmi chart) the error inside logic could be which the population is right and the bmi chart is incorrect.

37. Making time for yourself: Running = sanity. Alone or with neighbors it has fantastic healing results that last all day long bmi chart men. I find doing it early inside the morning is best as I learn I'll receive my run in and "lifetime stuff" throughout the day will likely not get inside the method.

So the index does get balanced by both factors and, total, it is actually pretty wise inside its intended purpose. To me, it is actually not critical which just 64% instead of 66% are overweight or fat, just that such a staggering percentage of the American population is. If calculated for woman minorities, the prevalence is even high, non-Hispanic black females is 79.6%, Mexican-American ladies 73% plus non-Hispanic white ladies 57.6%. It kind of flips for men with non-Hispanic white men 71%, non-Hispanic black men 67% and Mexican-American men74.6%.

Lets start with an average brick, like the multi-colored 1 at proper. We wish To create a little brick pile that has the same proportions as the initial brick, however, is twice because big in every three dimensions. First we add a brick, inside purchase to double the length. Then alongside that, you add two more bricks to double the width.

BMI refuses to measure body fat straight bmi chart women, nevertheless it relates carefully to direct measures of body fat. For adults, BMI is interpreted whilst factors such as sex or age are not taken inside account.

Let's break it down a bit. "Ideal body weight" is defined because the fat persons are expected to weigh for good health based on age, sex plus height. Body composition is the makeup of the body inside terms of fat-free mass (the piece of the body composition that represents everything but fat--blood, bones, connective tissues, organs plus muscles) plus fat mass (actual amount of necessary and non-essential fat in the body.) Essential fat is the amount of fat essential for general functioning of the body.

If you don't fall in the general range, then receive oneself checked with different appropriate techniques to figure out the amount of body fat. This will provide a greater perspective plus enable we to achieve or maintain your ideal weight.