2-integration-by-parts-how-mathbff

# Interactive video lesson plan for: ❤︎² Integration by Parts... How? (mathbff)

#### Activity overview:

MIT grad shows how to integrate by parts and the LIATE trick. More videos with Nancy coming in 2017! To skip ahead: 1) For how to use integration by parts and a good RULE OF THUMB for CHOOSING U and DV, skip to time 2:46. 2) For the TRICK FOR CHOOSING U and DV (the LIATE memory trick) skip to 10:12.

WHEN to use INTEGRATION BY PARTS: If you have an integral to evaluate, and you don't already know how to integrate it, as is, then see if you can simplify it somehow with algebra. If not, try doing a substitution, like U-Substitution. If U-Substitution does not help, then you may need to use the INTEGRATION BY PARTS formula.

RULE OF THUMB: The first step to use Integration by Parts is to pick your "u" and "dv". As a general rule of thumb, whichever factor in your integrand gets simpler when you take the derivative of it, make that your u. Then make the other factor your dv (and include the dx in this dv). Note: This works if the part you chose for dv does not get any bigger or more complicated when you integrate it. After you've picked u and dv, then find du by differentiating u, and find v by integrating dv. Finally, plug everything into the integration by parts formula and simplify.

TRICK: You can instead use an acronym memory trick to choose the right "u". The acronym LIATE stands for Logs, Inverse trig functions, Algebraic functions, Trig functions, and Exponentials (in that order). If you follow those letters, LIATE, in sequence, whichever type of function you find first that you have, make that your u. Then, make the next thing you find your dv. Once you've picked u and dv this way, the steps are the same as above. Find du by differentiating u, and find v by integrating dv. Then use the integration by parts formula and simplify for the answer.

Tagged under: integrate,integration,calculus,integration parts, parts,integrating,derivative,LIATE,choose ,dv,du,substitute,differential,differentiate,integral,indefinite integral,formula,definite integral,LIPET,ILATE,anti-derivative,khan,patrickjmt,-, , ,trig,log,exponental,algebraic,inverse trig,mathematics,equation,introduction,find,explained,intro,tutor,tutorial,tips,test,expression,function,math,problem

Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.

Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip

Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans

Play this activity

1. Students enter a simple code

2. You play the video

3. The students comment

4. You review and reflect

* Whiteboard required for teacher-paced activities

## Ready to see what elsecan do?

With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.

Quickfire

Carry out a quickfire formative assessment to see what the whole class is thinking

Discuss

Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices

Clip

Turn any public video into a live chat with questions and quizzes

### Spiral Reviews by Teachers and Digital Learning Coaches

@kklaster

Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech

Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks.

@ordmiss

Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral

@strykerstennis

Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks!