Trigonometric Substitution Example 7 (KristaKingMath)

How to evaluate an integral using trigonometric substitution.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[kristakingmath]

@brettbed Using a couple different softwares, one for the recording of myself and the screen, one for the slideshow presentation, etc. Glad you liked the video!! :)

[kristakingmath]

try 2 substitutions in row. do a u-substitution with u=4x, and then an s-substitution with s=cos(u)+4. that should get you to the integral of 1/(s^2), which you can evaluate and then back substitute into. hope that helps! :D

[kristakingmath]

You're welcome! Have you been able to go through the various examples on my website? :)

[kristakingmath]

you can substitute from the triangle... either way is correct, i just chose to do arcsec this time... but usually i use the triangle!! :)

[kristakingmath]

@wiskkeetango I always HATED when they skipped steps as well! Glad I could help. :)

[wiskkeetango]

Wow...excellent vid. after watching a couple of your trig substitution vids I'm pretty squared away on this stuff. I love how you explain the problem in detail. My textbook, larson 7th edition :( is soooo awful, I even have the sol. manual and it ALWAYS skips the steps I really want to see...THANK YOU.

[kristakingmath]

Hahaha, you just keep up going hard like a muggg and I know you'll do great on the test! :) As for changing the limits of integration, you can do it, or not, whenever you want! If you change the limits of integration, then you don't have to back-substitute at the end of the problem. If you don't change the limits of integration, then you have to back-substitute at the end before you plug in the limits of integration. Hope that helps!! :D

[slaughterkill]

I have a problem that involves trig functions, but not necessarily a trig substitution: "(integral of) ((sin(4x))/(cos(4x)+4)^2)dx"? I tried using a substitution with "w=cos(4x)+4", making "dw/-4=sin(4x)dx". I ended up getting "-.25 (integral of) (1/(w^2))dw", which brought me to ".25w^-1" which turns into ".25(cos(4x)+4)^-1". Does that sound like it would be correct? Oh, and then I solved it on the interval of 0 to pi/8, resulting in 0.0147, but my professor says the answer is 0.0125. Help? :(

[kerrymyles]

hey, Im over here in New olreans studying for my first Calc II test on integrals. I have 4 days. And i am going hard like a muggg...kinda like Lebron James, game 6, Boston! HA! Anyways that is irrelevant but this is not, When i do these trig sub integrals and they are definite trig sub integrals, why did you not change the limits of integration here? Have any tips as to when you are supposed to change limits in these kind of problems. Been of fan since last semester in Calc I. Now sub'd :)

[thethTone]

Hello, can you please briefly elaborate on what tips you off to what identity you put off to the side initially. sec^2thta-1. thank you.

[wiskkeetango]

Wow...excellent vid. after watching a couple of your trig substitution vids I'm pretty squared away on this stuff. I love how you explain the problem in detail. My textbook, larson 7th edition :( is soooo awful, I even have the sol. manual and it ALWAYS skips the steps I really want to see...THANK YOU.