Absolute value integral

In this video, I showed how to compute the definite integral of an absolute value function using the even or odd nature of the function for speed.

[@kingbeauregard]

Terrifyingly clear and efficient!

[@PrimeNewtons]

What a description! You win!!

[@josephparrish7625]

I LOVE this problem. I always spent a lot of time on absolute value in my pre-calculus class! Every time I watch you, I miss teaching so much!

[@jam9339]

Perfect explanation of the absolute value.

[@shandyverdyo7688]

I love you man! I'm also a maths teacher but got stuck when I want to discuss this integral of absolute function to my students. Thank you so much!

[@juliovasquezdiaz2432]

Excelente vídeo. Tengo 71 añitos, estoy conectado con matemáticas. Ahora recordando integrales. Gracias por compartir. Un suscrito a su canal. Saludos desde Perú.

[@jan-willemreens9010]

... A good day to you friend Newton, Again I saw a perfectly executed presentation on an absolute value definite integral, I followed exactly the same strategy (graphs are great tools in this case), as if we had the same math teacher in the past (lol). A small comment I want to make regarding the sign analysis between - 4 and 4 is, we know that - 1, 0, and 1 are zeros, and that there aren't any asymptotes present, so we know that at these points there will be a sign change left and right, this means that we only need to do one sign calculation, at least this is what I did ... thank you again master Newton for a very clear presentation delivered with great enthusiasm ... Take care my friend, Jan-W

[@PrimeNewtons]

Yes, yes, and yes!

[@jan-willemreens9010]

... Third time ' yes ' is the charm I believe Newton (lol) ... In Dutch language: " Drie maal is scheepsrecht " ... Have a nice day Newton, Jan-W

[@vincentmudimeli4430]

Your explanation iS wow

[@sy8146]

Thank you for explaining. If we use the (given formula) = 2 ∫(0～4) |x^3-x| dx, it is -2 ∫(0～1) (x^3-x) dx + 2 ∫(1～4) (x^3-x) dx = 2×(1/4) + 2(56+1/4), and the calculation is a little easier.

[@knolljo]

this is explained so well! looking forward to watching some more of your videos

[@lyndalekirk6883]

i love your dedication man keep it up

[@PrimeNewtons]

I appreciate it!

[@rsassine]

Just superb. You are a great teacher.

[@pedrojesus4967]

I know maths. I watch yours videos to learn english. You are the BEST!!

[@murdock5537]

Excellent, this is awesome, many thanks, Sir!

[@biswanathmukherjee4622]

Excellent and all wishes for peace and human growth.

[@28.rezanurikhsan23]

Thank u Sir! U help me to pass my test

[@chukwudisimere8463]

Awesome video... i love your videos and how simple and explanatory they are. Can you make videos on Partial differential equations please?

[@khaleddamha3127]

Great teacher

[@lovemolkalea5489]

I almost laugh with this sir😂, your great 🥳🥳🥳

[@arbenkellici3808]

Great explanation of the absolute value professor!

[@wtt274]

Thank you Sir for your very clear explanation ! ❤

[@technicallightingfriend4247]

Fundamental theorm of integral calculus We could use property p7 -a to +a If Integrand is even =2( lower lt 0 to upper lt +a) integrand differential At my answer is same (16×7) +1=113 unit square

[@SamoanFor4everxx23]

Splendid!!

[@jensberling2341]

Lovely presentation and persuasive

[@user-xw6ky8ob4l]

The name of your game is absolute Love with unrivaled excellence.

[@nothingbutmathproofs7150]

Here is a nice way of doing this without even making the chart, although you need the cut-off points that you found. Over each interval that you found, I integrate x^3-x for all of them. To make sure that you get the correct result, take the absolute value of each integral. That does make it faster.

[@zianiera]

Clear explanation

[@moonwatcher2001]

Awesome, mate ❤

[@orenaharoni8763]

10:15 I must say that this is the most beautiful integral sign ive ever seen

[@surendrakverma555]

Very good. Thanks 👍

[@drbalontotis2474]

you are legand bro 🤯

[@jamesjarvan7804]

So nice!

[@SarfrazAhmad-gg7iu]

Would you please explain why did you put inner function equal to zero . Btw your teaching method is ❤❤❤

[@jam9339]

Love it❤❤😮

[@dadle22]

Thank you

[@ahmedamr1124]

ten out of ten thanks alot

[@user-jo7nu2ur6n]

I integrated and multiply it by 2 the answer 112 . Why I didn’t get 113 ?

[@PrimeNewtons]

Your integration should give 56 ½ before you multiply by 2

[@stephenlesliebrown5959]

I also got 112 for the "fast way" (which took me more time than the "long way"!). I found out I needed two integrals of x^3 - x. First from 1 to 4 giving 56.25 and then from 0 to 1 giving -0.25. Now, to account for the absolute value nature of the problem that negative area has to be flipped over the x-axis thus becoming+0.25. So finally 2 ( 56.25 + 0.25) = 113. Whew. Best wishes to all for a happy New Year 🎉

[@tah_aki]

The eyes says a lot 😂😂❤

[@said14121]

رائع ❤❤❤❤❤

[@killing_gaming0973]

I got it right without help omg

[@honestadministrator]

| x^3 - x | being an even function Given integration equals to integrate [0, 4 ] ( x^3 - x) dx =2 ( x^4 /4 - x^2/2 ) = 2 * 4^3 - 4^2 = 4^2 ( 8 -1) = 112

[@richardbraakman7469]

You forgot that x^3 - x is negative from 0 to 1 :) So you need to split the integral at 1

[@honestadministrator]

@@richardbraakman7469 well integration ( a to b) ( Integrant_1 + Integrant_2) = integration ( a to b) ( Integrant_1) + integration ( a to b) (Integrant_2)

[@richardbraakman7469]

Yeah but you have to integrate -(x^3 - x) for the interval from 0 to 1, because of the absolute value operator

[@user-nd7th3hy4l]

J= 112 ua

[@romka2010]

He have a mistake “1.5 is not between 0 and 1

[@Treasure-rr3ui]

good teeth