integral of csc(x), the standard result, calculus 2 tutorial

Integral of csc(x), the standard result, calculus 2 tutorial

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#blackpenredpen #math #calculus #apcalculus

[krukowstudios]

1:02 “and then we still have the dx”
_writes down du_

[CLG]

These questions they ask in these classes. I'm supposed to know out of thin air to multiply by cscx + cotx. Good vid.

[CaesarCapone]

You know, this little trick of 1*x = x, where 1 can be ANY fraction where the numerator = denominator is always out of my grasp. I usually never think about that trick, but it sure comes in handy! Thanks blackpenredpen!!!

[diaz]

THANK GOD FOR BLESSING US WITH THESE PRICELESS VIDEOS

[eduardorivera]

AMAZING!! Haha! It was funny how it all ended up just being a simple 1/u integration. Thank you!

[Donivar]

You saved my day. I was solving an integral that, after using some trigonometric identities ended up becoming 1/sin x. The problem is that it was a defined integral and the values would result in undefined. So I changed my method and ended up with integral of csc(x) and couldn't figure out how to continue from there.

[jaipatel]

Error in notation at 1:03 ... should be dx GREAT VIDEO THOUGH KEEP UP THE AMAZING WORK!!!

[brianm.]

@1:30 he briefly transformed into blackpenredpeneraser

[张鹏飞-wv]

I am wondering how U can think about times (csc(x) +cot(x)) without knowing the result at the first place

[motheogodfreylekaba]

what i like about this proof is that when youunderstand it properly you can find the integral of secx as easy as

[beybladerocks]

It's 12:30AM, my assignment is due in 7 and a half hours.
Lifesaver.

[Vyantri]

Great video very helpful! By the way, I've been wondering what that ball he always holds when doing videos is? Is it a mic?

[Leeanne]

interesting to see that you will end up with a different answer if you multiply at the end by (cosec x - cot x) instead of (cosec x + cot x). Then your answer will be ln (cosec x - cot x).
Check: If you differentiate both answers, ln (cosec x -cot x) and -ln ( cosec x + cot x ) separately, you end up with the same cosec x.

[FlashVortex]

Really nice! small question though... how do you know what to multiply exactly? the first step.

[Abhinab_Kalita]

In your 2nd step it should be dx "which you have written as du"

[youcandoit]

If we multiply and divide by 'cosecx-cotx' instead of 'cosecx+cotx' then we would have got 'ln|cosecx-cotx|+c' instead of '-ln|cosecx+cotx|+c' which I know is the same but it looks nicer :P...

[adityaadit]

I didn't have enough intuition to figure it out... This helped me

[dynamix]

How u know that it should be multiplied and devided by cosecx + cotx

[fatimamohammed]

Thanks for explaining this neat trick! Why cant we just have -du = csc^2x+cscx * cotx dx. Then we sub it back in to the original integral and then thankfully everything evens out perfectly? Or is my assumption wrong somewhere?

[holyshit]

Integration of composition rational function and trig functions
1. Express integrand in terms of sec(x)and tan(x) or cos(x) and sin(x)
a) if we have function R(sec(x), tan(x)) substitute sec(x)=t-tan(x)
b) if we have function R(cos(x), sin(x)) substitute cos(x)=(1-sin(x))t