Monday, October 6, 2014

Advanced Math Solutions – Integral Calculator, substitution

In the previous post we covered common integrals. You will find it extremely handy here b/c substitution is all about simplification, transforming the function into something more familiar.
At its basic form, substitution is used when an integral contains some function and its derivative. It is the reverse chain rule (click here for a quick review).

The substation rule is as follows:
\int f\left(g\left(x\right)\right)g^'\left(x\right)dx=\int f\left(u\right)du,\:\:\:where\:u=g\left(x\right)

Let’s see how it works, starting with the logarithmic function (click here):


Here’s an example of exponential functions (click here):


Here’s an example using the power rule (click here):



Here’s an example using simple trig substitution (click here):


Sometimes the appropriate substitution is not that obvious and requires some extra work.  We’ll walk you through more advanced examples in the next post

Cheers,
Michal

14 comments:

  1. Even though the future seems far away, it is actually beginning right now. See the link below for more info.

    #future
    www.ufgop.org

    ReplyDelete
  2. Click on this link to get some more articles on this cool topic.

    ReplyDelete
  3. The Integral Calculator lets you calculate integrals and antiderivatives of functions online — for free! Our calculator allows you to check your solutions to calculus exercises. The Integral Calculator supports definite and indefinite integrals antiderivatives as well as integrating functions with many variables. Liteblue

    ReplyDelete
  4. Published over the 'employee id' words. It is your special recognition number. liteblue usps employee login It consists of an excellent remedy and also solution to the customers.

    ReplyDelete
  5. You need not to worry any more, we are here to offer you the best academic writing
    Solutions; order quality best writing service from us and learn how to purchase term paper today!

    ReplyDelete
  6. Ohh, great! I think your opinion is correct, thank you, I will follow you regularly!
    earn to die

    ReplyDelete
  7. Hi your blog is very interesting, You don't need to download Netflix account we provide you free of cost app and watch all free movies and TV shows with this app
    Online Show Box

    ReplyDelete
  8. It is possible to manage renewal and your subscription in your Norton account. norton.com/setup provides a Norton Utility tool to test and optimize your own PC to you. Norton utility is a completely free tool that could be downloaded by the manufacturer site. It increased the boot speed and optimize the overall performance of the system.
    norton.com/setup
    office.com/setup
    office.com/setup
    norton.com/setup

    ReplyDelete
  9. Amazing blog your blog is really good and your article has always good thank you for information.

    คาสิโนออนไลน์ที่น่าเชื่อถือและมีความเป็นมืออาชีพที่สุดในตอนนี้
    โปรโมชั่นGclub ของทางทีมงานตอนนี้แจกฟรีโบนัส 50%
    เพียงแค่คุณสมัคร สล็อตออนไลน์ กับทางทีมงานของเราเพียงเท่านั้น
    ร่วมมาเป็นส่วนหนึ่งกับเว็บไซต์คาสิโนออนไลน์ของเราได้เลยค่ะ
    สมัครสล็อตออนไลน์ >>> Goldenslot
    สนใจร่วมสนุกกับ คาสิโนออนไลน์ คลิ๊กได้เลย
    มีทั้งคาสิโนออนไลน์ หวยออนไลน์ ฟุตบอลออนไลน์ สล็อตออนไลน์ และอื่นๆอีกมากมาย

    ReplyDelete