Trigonometric Substitution Example 4 (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]

I'm glad you mentioned that, because I haven't heard of it either. I was going to research and try to see if I could find it, but I'm not sure if I'll be able to.

[kristakingmath]

I'm so glad I've been able to help! :D

[kristakingmath]

@RangerRandall Thank you so much! That makes me feel great! Please let me know if there's ever anything I can do to help you. :)

[kristakingmath]

@bodinian I'm sorry I didn't explain more. Please check out my video on how to set up trigonometric substitution problems if you want a more detailed explanation of the identity. It's one of three that are fundamental to this process. :)

[NerdBomber]

It truly is, I walked into class today and actually had an idea of whats going on now. I saw one of your comments on one of the other videos, saying how teachers have to rush things to fit class requirements. I'm a slow learner, and that's kind of what I have trouble with.

[HaidaSOD]

Wow, just a few minutes ago I was freaking out over this! Phew, I now fully this section and I'm ready for my midterm next week!
You taught me so much, I cannot thank you enough! Keep doing what you're doing and keep smiling 'cause you're awesome!
-Merna G.

[kristakingmath]

If it's really the square root raised to the 3/2, then you can simplify that to (25-x^2)^(3/4), which you can rewrite as the fourth root of (25-x^2)^3. you'll use the u=asin(theta) substitution, and if you solve that for x, you can substitute for the x in x^4, as well as inside your square root. Hope that helps get you going!! :)

[npip]

At 7:00, I would never say "tangent to the negative one". That means tan(x) to the power -1, which is 1/tanx to me. I'd always read tan^(-1)(x) as arctan because I can't bring myself to interpret "to the" as something other than an exponent; that's what it is.

[kristakingmath]

Oh cool! Okay... that makes sense! I'll poke around some more and see what I can find, and figure out whether or not I can do a video. Thanks for sharing this! :)

[kristakingmath]

The triangle is always like that because of the pythagorean theorem. if the opposite side is x and the adjacent side is 1, then they pythagorean theorem tells you that x^2+1^2=(hypotenuse)^2, so the hypotenuse has to be sqrt(x^2+1). I hope that helps make it a little more clear! :)

[kristakingmath]

I totally understand! I Hopefully watching videos at home before class will continue to help you feel more prepared. I think that order is a better way to learn things anyway! :D

[kristakingmath]

I don't have any videos on that! I will add one if I can! :)

[kristakingmath]

@xXMcBeanXx I'm so glad! And you're welcome! :D

[perlasantaolaya]

Thank you SO MUCH for all of the excellent explanations and examples. You have no idea how helpful they have been for me!!! Thank you Thank you Thank you!
XO Perla

[kristakingmath]

Because it will always reduce to what you're taking tan of. For example, arctan(tan(theta)) will reduce to theta, arcsin(sin(x)) will reduce to x, arcsec(sec(a)) reduces to a. Hope that clarifies things!! :)

[kristakingmath]

good luck on your test tomorrow!! i'll keep my fingers crossed for you!! :)

[kristakingmath]

You're welcome... glad it's helping!! :D

[kristakingmath]

Aww thanks! You're awesome too Merna! Go and rock the midterm! :D

[Rijksband]

Excellent! I was just getting round to this subject when you put this video up.One question though. (And I just answered my own question too :). As always, nice work.

[herrzyklon]

Hey there quick question, when you raised to arctan, why didn't the right hand side reduce to 1 instead of theta? Thanks loads