Looking for a Tutor Near You?

Post Learning Requirement »
x

Choose Country Code

x

Direction

x

Ask a Question

x

Hire a Tutor
Dubai

Integration By Parts

Loading...

Published in: Mathematics
141 Views

This is a lecture on integration by part

Faisal K / Al Ain

0 year of teaching experience

Qualification: MSc, BSc Math

Teaches: Mathematics, Statistics, SAT, Maths

Contact this Tutor
  1. Integration By Parts %ßeVgÆitÜtJii Faisal Khasawneh Faisal Khasawneh
  2. Integration By Parts Goal : To be able to integrate more functions Overview: In this sson, you will be introduced to another method of integration, integration by pa s. hile substitution helps us recognize derivatives produced by the chain rule, integration by parts helps us to recognize derivatives produced by the product rule.
  3. Integration By Parts Prerequisite Knowledge You should know: Definit ndefinite Integrals Ho to perform Integration by Substitution e product rule for derivatives
  4. Integral Derivative J x3dx= Integration By Parts Integral cos(x) sin(x) Derivcitive f cosxdx f sinxdx = sinx + c = —cosx + c
  5. Integration By Parts Let's start off with this section with a couple of integrals that we should already be able to do to get us started. First let's take a look at the following. So, that was simple enough. Now, let's take a look at To do this we 'Il use the following substitution: Let . Therefore, Again, simple enough to do provided you remember how to do substitutions
  6. Integration By Parts Now, let's look at the integral that we really want to do. Here, are multiplied together. o do this integral we will need to use integration by parts so let's derive the integration by parts formula. We'll start with the product rule.
  7. Integration By Parts Start with the product rule: This is the Integration by Parts formula.
  8. Integration By Parts - u is easy 10 d du = (X) dv is easv to inlegrate dv is eåsy to integrate etimes it is necessar to integrate to Integratewypparts more llan on arts more t an once enmes It IS necess
  9. Integration By Parts Guidelines for Selecting : (There are always exceptions, but these are generally helpful) "L-I-A-T-E" Choose "to be thefunction that comesfirst in this list: I: Logar• hmic Function I: I erse Trig Function : Algebraic Function T: Trig Function E: Exponential Function * *T & E are interchangeable **
  10. Example 1 : LIATE Algebraic factor Exponential du = dx dv = ex dx V = ex
  11. Example 2: LIATE Algebraic factor du = dx v = sin x
  12. Example: 3 LIATE u = Inx dv = dx Logarithmic factor du — x 1
  13. Example 4: f x2ev dr LIATE du = dx u = x2 dv = eXdr • —--fé-&d
  14. Example 5: LIATE u = ex dr v = sin x u = ex v du his IS the xpression we
  15. Example 5 cont. This is called "solving for the unknown integral." It works when both factors integrate and differentiate forever.
  16. A Shortcut: Tabular Integration Tabular integration works for integrals of the form: where: Differentiates to zero in several steps. Integrates repeatedly.
  17. f x-2ex dx 2 J x2ex x2ex Compare this with the same problem done the other way as in example 4: -2xex +2eX +C
  18. Example 4: LIATE fx2ex clx u = x2 dv=eXdx V = ex dv = eXdx du = dx This is easier and quicker to do with tabular integration!
  19. 1?3 ? - 3?2 + 6? 6 0 sin ? — cos ? —sinx cos ? sin ? —x3cosx +3x2sinx + 6xccsx — 6sinx+ ?
  20. Integration By Parts b, d. In(x) co 2x)e3X dx f xln dx

Need a Tutor or Coaching Class?

Post an enquiry and get instant responses from qualified and experienced tutors.

Post Requirement

Related PPTs

Upload PPTs

If you have your own PowerPoint Presentations which you think can benefit others, please upload on MyPrivateTutor. For each approved PPT you will get 100 Credit Points and 100 Activity Score which will increase your profile visibility.

Upload Now
Home > PowerPoint Slides > Integration By Parts