Integrating sqrt(x^2-2x)

[@MrLidless]

If you rewrite it as integrating (sqrt x)(sqrt (x-2)), you can set u’ = sqrt x, v = sqrt (x-2), and then use integral(u’v) = uv - integral(uv’) to quickly get to the answer.

[@xxxx015]

I did it my head lol, maybe im too focused on calculus

[@TSSPDarkStar]

Weird flex but ok

[@thomasblackwell9507]

Have a beer and relax!

[@JohnRandomness105]

After completing the square, I used the hyperbolic substitution: x - 1 = cosh u, sqrt(x²-2x) = sinh u. One needs to replace sinh²u with (cosh 2u - 1)/2. After integrating, one must replace sinh2u with 2 sinhu cosh u. One gets the same result upon recognizing that arccosh(x - 1) = ln(x - 1 + sqrt(x² - 2x)).

[@PunmasterSTP]

Square root? More like “Coolness to boot!” I remember these from my first calc class, and I always thought they were neat. Thanks for sharing!

[@SyberMath]

You're welcome!

[@leif1075]

@@SyberMath why would.anykne think to add and suvtract 1..i dont see why anyone would..why not do integration by parts?

[@ramaprasadghosh717]

√(x^2 --2x) = √((x-1)^2 -1) = tan(u) writing sec(u) for x -1 i.e dx = sec(u) tan(u).du Hereby given integration = integrate ( tan^2(u)sec(u) du) and so forth

[@nicogehren6566]

nice solution sir thank u keep it up

[@SyberMath]

Most welcome

[@WahranRai]

Where is the domain of x before starting ?!

[@moeberry8226]

You can find the domain easily by setting x^2-2x> or equal to 0. Factor out an X to start and you will obtain X(X-2)>or equal to 0 and check some numbers before 0 and between 0,2 and after 2. Then choose the positive interval or intervals.

[@WahranRai]

@@moeberry8226 I KNOW that, it is to tell him that he forgot to specify it

[@omar_5352]

Nice one, thanks. I solved it by applying (by part) twice to loop back to the same integral then simplifying. More fun than the trigonometric approach!😉

[@XJWill1]

Here's the missing link for the integral of powers of secant video: kzbin.info/www/bejne/gprSlmOtjKigjKc

[@SyberMath]

Thank you for sharing the link!

[@242math]

very well explained syber, thanks for sharing

[@SyberMath]

My pleasure! 💖

[@MohdIrfanZ7]

Please do videos on integrals also.

[@SyberMath]

This is a video on integrals

[@TSSPDarkStar]

@@SyberMath LOL

[@Qermaq]

Wish I knew calculus. It is beautiful, but I feel like a person listening to jazz knowing nothing about jazz. What's the best way for Algebra II and Some Trig champs like me to learn this witchcraft?

[@SyberMath]

Oh calculus is pretty straightforward. Get a good book and start reading: * The calculus lifesaver : all the tools you need to excel at calculus by Banner, Adrian D * Everyday calculus : discovering the hidden math all around us by Fernandez, Oscar E. (Oscar Edward) * Calculus Made Easy by Silvanus P. Thompson, Martin Gardner

[@Qermaq]

@@SyberMath I totally get the basic concept. I just wish I understood the lingo. Gotta love Martin Gardner, I should look that one up.

[@amitkumargs6564]

U can do it by integration by part within only 1 min

[@magick333]

integral of sqrt {(x-1)^2 -1} and trig substitution.

[@two697]

Hyperbolic substitution

[@holyshit922]

@@two697 Maybe Euler's substitution In this integral it will not be so much calculations

[@two697]

@@holyshit922 I don't like integrating sec^3 so I prefer hyperbolics

[@angelmendez-rivera351]

@@two697 No secants in Euler's substitution

[@giuseppemalaguti435]

+1,-1 e poi secante

[@NaseerAhmad-dd6pp]

Suppose you initially catch 500 drones, tag them, and release them. At some point later you re-catch a new 500 drones, and find that only 300 of them are tagged. Assume drones were equally likely to be caught at all times. 1) What is the smallest number of drones that might be out there? i.e., what is the smallest possible number value N might have? 2) What was the probability of this occurring (these specific catch totals) as a function of N? 3) What number N maximizes the likelihood of these results? 4) Re-do numbers 1, 2, and 3 in the more general setting, with N as the total number of drones, n1 as the number caught and tagged the first time, and n2 caught and tagged the second time.

[@PunmasterSTP]

@@carlgauss1702 Yeah I was wondering what this had to do with the video before it dawned on me seconds later that it was homework!