ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Calculus demystified for Real People, Part 4 -- Formulae Rearranged

Updated on May 4, 2013
Source

Integration By Parts

Since we started to study ourselves this crazy math..we wanted to find ways to simplify 'Heuristically' using easier Methods and our own Mnemonics instilled in us by our Tutor... That our Dad got us in Junior High. Lucky us right?

Using some rules of Calculus and rearranging formulas we can attack more complicated problems that will arise in the life of a College dude, you know?

STRAIGHT TO our Subject



The Equation to the right has a derivative g′ that could be a handicap since we usually see more down to earth functions that multiply themselves as in f(x).g(x)

If we really need a practical formula for

∫f(x).g(x)dx

We postulate a new arrangement as in the formula below. You can obtain this new formula by Integrating both sides of the equation


We've got to make sure that f can be differentiated to f′

and g be able to get integrated as well...


EXAMPLE :

We should know that ∫(1/x2)dx = -1/x

and ∫x-1dx = ln/x/ +c

Consequently Inversely , we can asses that:

(ln x) ′= 1/x ( differentiation of natural logarithm for x)

Let's say we want to integrate this function....we know beforehand that we can break it down...

We rearrange it to our formula of 2 functions

∫(lnx)(x-2 )dx= lnx ∫x-2dx- ∫ f′ (∫g)dx

where f′ equals to 1/x

and g integrated (∫g) equals to -1/x

replacing in the formula for integration of two functions of the type ∫f.gdx=??

we get the easier to solve equation:

The answer is

-lnx/x -1/x

or -(lnx+1)/x

You should know by now that

∫x^k or ∫xk = xk+1/k+1

and inversely

(xk)′= kxk-1 (differentiation of a power)





Comments

Submit a Comment

  • JT Walters profile image

    JT Walters 

    6 years ago from Florida

    Lord,

    You are doing a great service to the kids!! Man you are prolific.

    JT

  • Lord De Cross profile imageAUTHOR

    Joseph De Cross 

    6 years ago from New York

    Thanks JT,

    We did this one on our break time from our poems...! We believe we are doing a great service to our young kids!

  • JT Walters profile image

    JT Walters 

    6 years ago from Florida

    Hey Lord,

    Some nice ratings and the hub will be good for a while as Calculus hasn't changed since Euclid. I have my Calculus book for Engineers in the car. I don't remember this part of Calculus but it has been a few years. I'll have to go back and look it over.

    Great hub. Very educational and it will inspire a lot of young people to take higher advanced Math classes!!

    Awesome and Vote Up!! JT

  • Lord De Cross profile imageAUTHOR

    Joseph De Cross 

    6 years ago from New York

    Oh Victoria and Tammy!

    Ha-ha-ha! You are such a wonderful...like a far away family to Lord. You guys got me laughing hard too! Is just a hub for the average kid..who is spending Christmas at home...and maybe...he has some little confidence in himself. This hubs were asked by JT Walters; shame on her...she is watching the news(meet the PRESS), and she left me with this Calculus 'thing'

    LORD

    Hey! was joking JT

  • Victoria Lynn profile image

    Victoria Lynn 

    6 years ago from Arkansas, USA

    Well, my Lord, I gave you an awesome on this one. It must be awesome. It's Greek to me, though. I'm amazed at your talents--Calculus, poetry, and you even threw in a few recipes of late....I'm sure this hub will be very helpful to the masses who study calculus. As for me, I think I'll go over to one of your algebraic hubs, instead. :-) Good job! I am duly impressed.

  • tammyswallow profile image

    Tammy 

    6 years ago from North Carolina

    Well.. we now know who the genius of the group is. :) I was going to check useful but who am I kidding. I will pass this on to my son who is an engineering major and in calculus now. Well done, beautiful fonts!

working

This website uses cookies

As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://hubpages.com/privacy-policy#gdpr

Show Details
Necessary
HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
LoginThis is necessary to sign in to the HubPages Service.
Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
AkismetThis is used to detect comment spam. (Privacy Policy)
HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
Features
Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
MavenThis supports the Maven widget and search functionality. (Privacy Policy)
Marketing
Google AdSenseThis is an ad network. (Privacy Policy)
Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
Index ExchangeThis is an ad network. (Privacy Policy)
SovrnThis is an ad network. (Privacy Policy)
Facebook AdsThis is an ad network. (Privacy Policy)
Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
AppNexusThis is an ad network. (Privacy Policy)
OpenxThis is an ad network. (Privacy Policy)
Rubicon ProjectThis is an ad network. (Privacy Policy)
TripleLiftThis is an ad network. (Privacy Policy)
Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
Statistics
Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)