Welcome to Clip from Spiral logo

Interactive video lesson plan for: ❤︎² Trig Substitution... How? (mathbff)

Activity overview:

MIT grad shows how to integrate using trigonometric substitution. More videos with Nancy coming in 2017! To skip ahead: 1) For HOW TO KNOW WHICH trig substitution to use (sin, tan, or sec), skip to 0:18. 2) For how to do a SIN SUB and WHEN TO TRY TRIG SUB, skip to 1:29. 3) For a TAN SUB with the radical in the NUMERATOR, skip to 14:41. 4) For a SEC SUB with a RATIONAL/FRACTIONAL POWER, skip to 22:36. 5) For miscellaneous types, skip to time 24:54.

For my video on how to do BASIC INTEGRATION, jump to: https://youtu.be/49FfXVOIalE
For my video on how to integrate using U-SUBSTITUTION, jump to: https://youtu.be/kTXnhwQKuvU
For my video on how to do INTEGRATION BY PARTS, jump to: https://youtu.be/pqKs3zcqJwU

HOW TO KNOW WHICH trig substitution to use: If the x-expression under the radical has the form of "a number minus an x^2 term", then you'll use a SINE substitution. If it has the reversed form of "an x^2 term minus a number", then you'll use a SECANT substitution. And finally, if the expression under the root is addition (the form of "an x^2 term plus a number"), you'll use a TANGENT substitution.

WHEN to use TRIG SUB: If you have an integral with a radical expression in it, and you know you cannot integrate using: a Table of Integrals integration rule, or using U-Substitution, or using the Power Rule, or using other integration techniques like Integration by Parts or Partial Fractions, then it is a good idea to try trig substitution.

HOW TO DO TRIG SUB. Here are the main steps of trig sub: 1) Decide which trig substitution you need [x = asin(theta), x = atan(theta), or x = asec(theta)], filling in the value for "a". 2) Simplify the radical expression by plugging in your substitution for x in the radical [For ex. for a sin sub, plug in for x in sqrt(a^2-x^2)]. 3) Find dx from your x substitution. 4) Substitute into the original integral, replacing the radical, the dx, and any other x factors, with the theta expressions you found. 5) Simplify and integrate, using whatever technique you have to use. 6) After you integrate, it's still in terms of theta. So the last step is to get it all back in terms of x. Draw a right triangle off to the side, label the sides with what you know from your trig substitution expression, find the third side, and use the sides of the triangle to get an expression for whatever trig function you need in your final answer.

Tagged under: trig ,trig,trigonometric,substitution,integrate,integration,integral,substitute,differentiate,radical,sin,tan,sine,tangent,secant,calculus,khan,patrickjmt,integration rule,sin substitution,tan substitution,sec substitution,-substitution,absolute ,rational,fractional,numerator,formula,trig integrals,indefinite integral, triangle,pythagorean indentities,anti-derivative,-, , ,intro,function,find,problem,math

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

Share on:

Share ❤︎² Trig Substitution... How? (mathbff) on Google+ Share ❤︎² Trig Substitution... How? (mathbff) on Twitter Share ❤︎² Trig Substitution... How? (mathbff) on Facebook Pin ❤︎² Trig Substitution... How? (mathbff) Email ❤︎² Trig Substitution... How? (mathbff)

Ready to see what else Spiral logo can do?

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


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


Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices


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

1000s of teachers use Spiral to deliver awesome, engaging activities that capture students' understanding during lessons.

Now it's your turn Sign up

Spiral Reviews by Teachers and Digital Learning Coaches

Review of Spiral by teacher: Kathryn Laster @kklaster

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

Review of Spiral by teacher: Room 220 Math Stars @3rdgradeBCE

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

Review of Spiral by teacher: Miss Ord @ordmiss

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

Review of Spiral by teacher: Adam J. Stryker @strykerstennis

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

Review of Spiral by teacher: Dr Ayla Göl @iladylayla

A good tool for supporting active #learning.

Review of Spiral by teacher: Brett Erenberg @BrettErenberg

The Team Up app is unlike anything I have ever seen. You left NOTHING out! So impressed!

Get the Clip Chrome Extension & Create Video Lessons in Seconds

Add Clip to Chrome