Integral of cos(x)*cos^-1(x) from 0 to 1

I will show you a wrong way to do the integral of cos(x)*cos^-1(x) but it gives the correct answer. A good trig integral to show calculus 2 students.

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[blackpenredpen]

It's only 12:56am for me! Integrals don't sleep!


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[neilgerace]

Hahahaha that's hilarious! It's like writing 16/64 and cancelling the 6s out.

[latt.qcd]

cos(x) * cos^-1(x) = cos(x) / cos(x) = 1.
So, the integral is 1 - (-1) = 2.
Obviously.

[bencheesecake]

This style of video is a lot of fun, and that sense of humor is part of what got me into math. Keep up the good work BPRP!

[spacelightning]

10/10 plot twist, would send to M. Night Shyamalan

[alexdemoura]

The Patrons LOVE it. They got 3 "BIG THANKS" end titles in a single 6:53 video.

[jeremygalloway]

What is the big ball mic thing in his hand? New subscriber...watched a few videos and he always is holding that. Always makes me think of him holding a glass of whiskey or gin. Just sloshing it around a bit...sipping it every few mins while writing on board with blackpenredpen. Not drunk...just sipping...chillin...doing some calculus.

[doctor]

What I did was add 0=cos(x)*(-pi/2 + pi/2). The distributive property turns cos^-1(x) into cos^-1(x)-pi/2, which is an odd function. Even functions times odd functions are odd, so, (cos(x)*(cos^-1(x) - pi/2)) integrates to 0, and we just integrate cos(x)*pi/2 on -1 to 1.

[stewartmoore]

I wish all of my math teachers adopted your style. You know, that math is FUN. I think a lot of teachers forget to include this. I know teaching is hard, and far be it from me to criticise something I've never done. But purely as a student, I know what works and what doesn't. And this works. I will be sending my lecturers your videos when I go back to uni next week. We'd have so many more mathematicians if more teachers were like you.

[thesecretguy]

You can tell who's actually watched to the end because loads of the comments say: 'yeah but the answers are the same though'...

[FotisValasiadis]

oh boi, here we go again solving integrals in paint.net

[Kanal]

The first way was the wrong way but its result was right result. It's so wittiy and funny and nice.

[saurabdhir]

Heres also a nice integral
∫(sinx+cosx)/{sin^4(x) + cos^4(x)}

Enjoy 😊

[Vandarte_translator]

It's 3 am. Why?
Now I gotta keep awaken.

[joshuamason]

I know it's a maths video, but I just have to point this out; you can't always use "isn't it" to make a tag question, you have to use what you asked to answer it(用什么问就用什么答). For example, if you want to make a tag question from "we have to subtract" (52 seconds into the video "BEST FRIEND"), you have to say "don't we" because the subject is "we" and the action is "to subtract", which contains a "do" verb. So to make a tag question, you have to first take the action, which in most cases are "do" and "be(is, am, are)", and put it in the negative form and add it to the subject. For example, to make a tag question from "we are humans", you take the action, which in this case is "be" in the form of "are", and make it negative which is "aren't" and add it to the subject which is "we", and that yields "aren't we?".

[thelightningwave]

Please make a video on why the inverse of even functions are not even.

[himanshumittal]

Hey there!
I solved the integral a bit differently.
#Cos^-1(-x) = pi - cos^-1(x).
Comes out to be the same!!
Ans: pi*(sin(1))
Thanks for sharing the integral🙏🏻

[Philgob]

is the odd even function thing a part of the normal curriculum? i’ve done calc 1-2-3 and i don’t remember that at all

[VibingMath]

wow this question has so many traps! Nice video man and your new arrangement on patreon support list in the video is cool too! 😁👍

[agabe_]

That was the most "trollest" math video i've ever seen