Calculus II: Trigonometric Substitution

In this video, we discuss the method of Trigonometric substitution for evaluating integrals.

00:00 - Introduction
00:11 - Method of trigonometric substitution
02:16 - Example 1
13:12 - General substitutions
16:28 - Example 2
26:55 - Example 3
36:39 - Example 4

[Mikebigmike]

brilliant video and thank you for making it, if you want my unsolicited advice I would suggest just slowing down a little bit, remember you're attempting to teach a new subject to people it's not a maths competition aha! just maybe clarify a little bit more with the steps you take and explain why it's allowed. but yeah overall a good video with good examples. thank you!

[jasonmantri]

cloudy, keep up the awesome work. I had a question about trig sub. We only create the triangle for the respective trig sub, correct? And also for stuff like sqrt(x^2+#) or (#-x^2), we want the substitution to be asintheta which is like the square root of that # I'm assuming? Because that is how I am seeing it for the substitutions. Thank you!

[anwarosman]

38:55
You have u = x+2, and put u for the numerator. But the numerator is x-2, Is this mathematically correct?

[jamesbike]

at 42:48 wouldn't it have been simpler to use a Pythagorean identity instead of the double angle?

[anshumandas]

10:42 Can we just write theta = arcsin x and replace everything in the last step in terms of arcsin?