integral of x*sqrt(1-x^4), trig substitution, calculus 2 tutorial

[@maksnowakmaks1819]

Wow!!! That was AMAZING! You just blew my mind! Thank you for the explanation, it was just what I've been looking for!

[@sheylaroblesrodriguez7437]

I was trying to solve this, but I couldn´t... Now, you helped me, thank you so much!!!!

[@vincentochieng9698]

You are an excellent teacher. I got helped a lot. Thank you

[@aastha3428]

After substituting u , I used the identity integral of sqrt(a-x^2) = x/2 sqrt(a-x^2) + a^2/2 sin^-1 (x/a) +c and got the answer within 2 minutes . Memorizing identities ,though nerve racking, sure has its perks.

[@ernestosaboia]

Great help, buddy!!! Thanks for all your videos

[@andrewmaksimovich2432]

This is so helpful, I don't know how I would survive my class without this

[@gabrielsalazarbustillos8592]

thanks man, 2021 at 1:11 am, saving my life

[@saxbend]

I love the way you pronounce Hypotenuse. :)

[@cheks_765]

This exact question was on my quiz earlier today. If only the algorithm would have recommended it sooner :(

[@atmsc4nd4l]

when i saw the thumbnail, trigo sub is the method that comes to my mind.

[@eness26-h1g]

thanks sir that was helpful

[@gokharol]

I came across this problem in a James Stewart and have spent a great deal of time trying to solve it but couldn't do it :-( I wanna thank you for sharing the solution. I guess I had to have an advanced vision to be able to think of this....unfortunately not this time

[@kaustavchakraborty811]

integrate 1/sqrt(1-x^4) between limits 0 to 1.

[@jimyjofred3540]

explicas tan bien que no hablo muy bien el ingles y te comprendo muchas gracias

[@chorobatestopografia7689]

IMPRESIONATE

[@joansgf7515]

I got the same answer using x=sqrt(sin(theta)), nice!

[@braedenrubin4234]

This uses so many levels of mathematics it's incredible, I mean it's integration, u sub, trig sub, power reduction, trig identities AND fundamental trigonometry😂

[@guardiadiego1137]

yeah6 you learn them all in elementary sch6ool

[@AniketBaniket]

@@guardiadiego1137 i doubt you were doing calc 1 in 8th grade

[@investingpioneer]

Elementary School? You must be a late bloomer, though I feel a sense that you're bragging. Indeed, preschool is the time to get a head start on such matters.@@guardiadiego1137

[@mariogabrielsalvatierrafra4500]

good one, thanx for sharing it

[@yesmanic]

How can I do this using riemann sum?

[@sebastianfernandezmora5796]

why you hold a mini death star?

[@blackpenredpen]

Sebastián Fernández so u could leave a comment like this :)

[@MC-mx1mt]

@@blackpenredpen he purposely asked that question so that you could reply him that answer

[@mhammedtomy545]

You are wonderful thank you keep doing these amazing videos . Again thanks

[@sarojkhanal7257]

Answer this pleasee. Isnt square root of (1-sin^2theta) modulus of costheta? Why did you write just costheta

[@odobenusrosmarus6035]

i think its because cos^2theta is always positive, so we dont need the modulus

[@bonbonpony]

Why is the next video in this playlist private?

[@blackpenredpen]

Bc it's private.

[@bonbonpony]

blackpenredpen So why is it listed on a public playlist? :P (Also tautology is not really an answer ¬.¬ )

[@julioalexandre9]

Integral of ((x^4 + 1)^(3/2))/(x^2) ?

[@jonathanmalagonnabor1762]

thanks a lot, you are the guy :^)

[@przemysawkwiatkowski2674]

Why sqrt(cos^2)=cos ? Why not |cos| ?

[@halden3014]

it is. but with integrals we dont evaluate the absolute values because we only care about the answer.

[@alexting827]

It is, but in indefinite integrals we assume it to be |cos| to be positive. When doing definite integrals, you have to look at the bounds to determine how to drop the absolute value bars

[@HieuLe-my2qm]

Thanks a lot

[@vincenciussufijanhadi1287]

How if, integral (4 + x^-1)° 1/2 dx. x = 0 to x = 1. This is length of curve

[@ayoubsbai6339]

2:29 is that a JoJo reference ?

[@rosaangelicamarinez5689]

thanks

[@CeceMelchor]

Thanks!

[@peacegaming3691]

Please solve 1/x sqrt (x)^4-1 answers

[@kahnsinho]

thx bro

[@rhivanaashari3903]

Ily 3000

[@peacegaming3691]

1/x sqrt (x)^4-1 answers

[@tarotymagia22]

thaankkkkssss

[@bhabatoshbarman4440]

anyone help integration of (1+X^4)dx

[@void2509]

definitely not x + x^5/5

[@yusupovjasur]

Genius!

[@NoNameAtAll2]

why did you write sin^(-1)(u) rather than arcsin(u)?sin^(-1)(u) can be interpret as 1/sin(u)=cosec(u), which is wrong in this integral...

[@227morgan3]

(sin(x))^-1=1/sin(x)=csc(x), but sin^-1(x) in that notation always refers to arcsin and NOT cosecant

[@gr1nder07]

nah man, in maths by the time you get to calculus it should be understood that "sin^-1" does not equal (!=) "1/sin" but is instead inverse sin. Arcsin isnt standard notation, just an adapted one that some people find easier

[@227morgan3]

gr1nder07 You're saying the same thing I was. It is just a question of whether the ^-1 superscript is written between the sin and x (meaning arcsin/ sin inverse, plug in a ratio and get out an angle), versus putting the ^-1 after sin(x) (i.e. (sin(x))^-1) is saying take the whole thing sin(x) and raise it to the negative first power, which is equivalent to csc(x)

[@blackpenredpen]

Yes, you two are both right. I think gr1nder07 were just trying to support and strengthen your very first statement. Especially I agree with " .. by the time you get to calculus it should be understood.." Thanks for watching btw! = )

[@AlgyCuber]

what about arcsin^2(x)? it will be arcsin^-2(x)

[@mmebled31sansnom26]

xiéxié xiexie very lesson