Trigonometric Substitution Example 3 (KristaKingMath)

Trigonometric Substitution calculus example.

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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]

It depends on which trigonometric identity you are using for the substitution, sin, sec or tan. Each one of the substitutions has its own triangle, and the value of the opposite and adjacent sides and the hypotenuse will change accordingly.

[kristakingmath]

if you have a^2-x^2, you substitute x=asin(theta). if you have a^2+x^2, you substitute x=atan(theta). and if you have x^2-a^2, you substitute x=asec(theta). hope that helps! :)

[kristakingmath]

SO awesome!! That makes me really happy! :D

[MinesFavorites]

my homework has been just officially and perfectly solved + total understanding ^_^, so thankful miss .. HUGE thanks to you

[billtheisen]

THANKS KRISTA FOR THE REFRESHER ON TRIG SUB. YOU MAKE IT LOOK SO EASY. GOOD EXPLANATIONS. VERY IMPRESSIVE, LIKE ALL YOUR VIDEOS. THANKS VERY MUCH. BILL T.

[kristakingmath]

@Musiclo0ovee You don't always, but if you get to the end of the problem, and you have sin or cos or tan, etc., left in your problem, you can use the triangle to figure out what that is, and simplify it. You won't always use it, but it's nice to have it ready to go when you do need it! :)

[kristakingmath]

i hear ya! don't worry tho, they get easier with practice. :)

[RSPSify]

why couldn't you solve the integral sec(theta)^3 using integration by parts?

[kencha]

how come we need the little triangle everytime? thx

[ronelmanzo]

can u explain further about the integrand of 4[sec^3(theta)d(theta)

[mark]

hi, why is it that other substitute with hyperbolic a.sinhx when the x^2 term comes first and you substituted with a.tanx

[dominikb]

You deserve some chocolate for the good work You are doing;)

[kristakingmath]

LOL, best comment ever!! I agree (because I love chocolate)!! :)