integral of (sin^-1(x))^2 *hard integration by parts*

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#blackpenredpen #math #maths #trigonometry #calculus #tutorial

[blackpenredpen]

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#blackpenredpen #math #maths #trigonometry #calculus #tutorial

[Idunge]

Bro you're too dope👏👏👏, thanks man. This was really helpful...

[joanolaetasoriano]

Good video. Were the results of the reduction formulas used in this procedure?

[comradepeter]

I think substituting t = arcsin(x) makes it much easier (as more people are familiar with the normal trig).
=> sin(t) = x
=> cos(t) dt = dx
=> integral (arcsin x)^2 dx = t^2 cos(t) dt = t^2(sin(t)) - 2t( -cos(t) ) + 2 (-sin(t))
=> integral = t^2 sin(t) + 2t cos(t) - 2 sin(t)

[nitnelavspetorials]

Very nice video! It helped me at my Maths homework so much!

[lotus-bird]

you're very charismatic, thank you for the video.

[moroccaninsider.DarSsiba]

Thank you for the video very helpful keep up

[rimman]

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[bonbonpony]

Hmm... I see this pattern appearing quite often in integration by parts, which is more evident when using the tabular method (aka the DI method): we approach some result in the I column that is harder to integrate but easy to differentiate, and we have to use the integration by parts again with this particular result.
But... this means that this result will then go into the D column, while the other one from that row will go into the I column.
Doesn't it remind you something? :q
Because to me, it kinda does! :> The *Euclidean Algorithm* for finding the *greatest common divisor* :q In this algorithm, we also use two columns (one for the numerator, and the other one for the denominator), and we subtract one from the other as far as we can; and when we can't subtract anymore, we _switch the columns_ and go on with the old spiel :J
This makes me wonder: Couldn't we do just that in the DI method as well somehow to solve it with just one table? We would have to mark the moment we switched the columns somehow though (maybe by drawing a squiggly line between the rows? :J ) and account for the column switch when putting down the result, too... Hmm...
Nevertheless, it makes me wonder about the possible connection between this and the Euclidean Algorithm. They're both division-like problems after all: in the integration by parts, we integrate a product of two functions to split it apart into its factors and integrate them separately (it's like the product rule in reverse), so maybe the connection isn't that far fetched? :q

[kathrynhill]

THANK YOU SO MUCH YOU ARE GREAT AT EXPLAINING THIS CONFUSING STUFF

[MShazarul]

This is great with DI method, thanks!

[GraphmetriCreatorTutorial]

Arc sin²x apakah sama dengan (arc sinx)²

[maudwitmeyer]

It helped me a lot !! Thank you very much :)

[georgeveropoulos]

hi i m looking the integral asin(x)^2/x over [0, 1]

[manolete]

shouldn't it be -1/2 times sqrt1 - x^2? I am referring to v in the second integral

[gabrielsegatti]

that was very good man, thanks for helping!

[ssdd]

ur integration by parts is confusing me

[samibaheru]

Differtiate your answer if your answer is right.

[ernestschoenmakers]

Well i used u=arcsinx and came to the same answer.

[beatricelajeunesse]

i could mary you right now, you are the best