Integration Using Inverse Trigonometric Functions - Ex 2

[Moh20ish]

That was awesome ^_^

I have a similar example like the one that u solved

it is the integral of (xsinx dx/(1+cos^2) )

I couldnt solve it

so can u solve it for me ^_^

[Keinlicht]

awesome shit. subbed

[kurniautami]

thanks :)

[kurniautami]

THANKS :)

[pgeske]

When you plugged in u, you also said that -du=sinx dx. aren't you supposed to solve for dx? so, dx=-du/sinx. shouldn't you then plug in -du/sinx to replace the dx? you just plugged in du for dx. i'm confused.

[patrickJMT]

@pgeske i never solve for dx when i do substitutions; just my style, some people do. algebraically it is all the exact same thing

[pgeske]

@patrickJMT Ah, okay. great video!

[ILoveCristianoR]

hey patrick, will you marry me? ;)

[patrickJMT]

@ILoveCristianoR i don't think my wife would approve of that : )

[mfrancoo27]

how do you know which trig function to use for u? why did you choose cosine?

[Keinlicht]

@mfrancoo27 Because the derivative of cosine is sine, thus du=sin(x)dx and the sin(x) on top disappears during the substitution.

[shadybot360]

This video is very helpful...hope that you have also for addition integrals...

[kenikozo]

Your website is a goldmine!

[mrhozer]

When do you need to change the limits of integration????

I'm so confused because on most other integrals you don't need to change the limits, even if you use u-substitution... So when do you need to change them?

[patrickJMT]

@mrhozer new variable, new limits. switch back to original variable, use original limits

[mrhozer]

@patrickJMT So do you always need to switch all the variables in the function to the terms of u when you do u-substitution?

[patrickJMT]

@mrhozer techincally you should always change the limits of integration when you do a substitution. if you leave the original ones, you are most likely writing something that is no longer equal. you may do it correctly at the end but you are writing incorrect statements.

[mrhozer]

@patrickJMT Thanks!!! I'll have to pay closer attention next time I come across a definite integral.

[rapz94]

@patrickJMT in 1=tan(x), instead of using pi/4, could we use pi/3? pi/3 is something like 1. 04

and pi/4 is also something like 0.7

[mitchy870]

I can feel it! I know I'll be having good grades again in math, in our integral calculus subject! :D

[patrickJMT]

@mitchy870 good luck : )

[ebadamageplan]

For arctan shouldn't X be (-pi/2, pi/2) not [-pi/2, pi/2]?

[weatherallc05]

if theres anything worse than inverse trig, its hyperbolics hehe

[mahlakeshmiri]

Honestly Patrick, you should write a textbook.

[utsawin09]

i hope youtube is paying you welll.....

[JuliaHalfJew]

You are awesome :) Thanks for helping out, and holy crap you have videos about everything! The AP test is tomorrow, you've probably got a ton of hits today on all calc videos :p

[geekgal1000]

you helped me so much patrick that i wrote you a llittle song. it goes like this:

"patrick rox! patrick rox!" x 96

sung in no particular tune as long as the volume steadily increases throughout.

[patrickJMT]

@geekgal1000 ha!

[geekgal1000]

@patrickJMT wow. i feel like a celebrity just replied to me. *faints.

still think i bombed the calc test today. sigh.

[patrickJMT]

@geekgal1000 sorry to hear the test may not have went that well : ( if it makes you feel any better, i had some less than stellar calc tests as well. it is all part of it (unfortunately)

[biiNo809]

thanks...would it be the same to use these formulas if they apply?

arcsin(u/a)= ∫(du/(square root of a^2-x^2)

(1/a)arctan(u/a)= ∫(du/a^2+x^2)

(1/a)arcsec(|u|/a)= ∫(du/u*(squareroot of)u^2-a^2))

[TheDrastic2014]

Oh my, I absolutely loved this video compared to most others. Thanks and please make more in your free time!

[TheBeefBowl]

Thanks really!

[Cooterstube]

math nerd fuck...

[patrickJMT]

@Cooterstube i just did

[Charlie135i]

what about ∫ArcSec(x) dx ????

[eoterm]

can you do an example or two where you have to complete the square or where there are thigns like sqrt of 1 -(lnx)^2

love your vids

[adiboy0909]

sir give me some tips on how to solve it in easier way.. thanks. !

[shinril]

why is inverse tan (1) equal to x? while it can just be subtracted directly to inverse tan (1) - inverse tan (0) = pi/4??. i wanted to know clearly why he assumed to input something to X?. i need help in calculus please help me.

[rohannesburg]

for a quicker way of integrating - like the example see if u can find the derivatives of eachother, in this case d(cosx)= - sinx, now since thers a -ve sign (representing the constant -1), you multiply the integral by -1 on the inside(numerator) and -1 on the outside of the integral, hence then substituting -sinx=d(cosx) back, making the subject the same which means: d(u)=d(cosx), and hence u^2 = (cosx)^2, and then completing the integral

hope this helps :)

[009mais]

you forgot the -ve sign dude

[giffffty]

savage!tanks a mill! nd btw i think the ans should be (- pi/4) u forgot about your negative 1 on top that you pulled outside @ 1:42!thanks again!

[dual85]

I will second calls you should write a mathematics textbook for Calculus. And you need a donate button in your channel!

[OneNOnlyInder]

man you are saving my life with these videos..

i have a calc final coming up in 2 days and i needed help

and this is making everything so clear!

thanks sooo much buddy!

[OneNOnlyInder]

man you are saving my life with these videos..

i have a calc final coming up in 2 days and i needed help

and this is making everything so clear!

thanks sooo much buddy!

[kelmopro]

u saved my calculus grade man! i found these videos really really helpful.

simple and to the point.

hellos from Puerto Rico & keep up the good work you're awesome

[kingofdice66]

how about (sinx)^2 * (tanx)dx now that is a problem

[packer083]

great stuff i took cal last year in high school and im just brushing up a little before i head off to school next week thanks a lot.

[patrickJMT]

you are welcome.

i have most stuff for calc 2 and tons for calc 3, so i will still be here if u get stuck!

[halokittyzzzz]

this guy does not ask for subscribers does not ask for money all he wants to do is just to help calc students. respect!

[winzera]

thank you very much for you help

[humorsvang]

I really like your videos! It was a bit hard for me to learn from Calculus the substitutions and so on, and our teacher isn't explaining as well as you do, so this is really good! It is a lot easier than to read it in a book too, because you explain in a simple and slow way. :)

[14jlim]

i hope you know you help alot of students that are learning calculus, thanks

[thematrate]

you should have wrote tan(0)=0 at x=0

[IrishPrid3]

your videos are saving my life right now, write a calculus book and send it to me please!

[fandanstan]

@IrishPrid3 I know! All these textbooks have all this technical crap that they don't even explain. We need a textbook that can actually help us LEARN.

[OpethMC]

Thank you, I find your videos very useful I am now starting Calc 2

[Joshiraxd]

you have no idea just what a great help these videos are!! im studying chemical engineering and my days are exhausting! comming home and learning from the text book can be real tedious at times. thanx to your videos, it doesnt take me much time at all to grasp these concepts. thanx dude you rock!!

[Syruscleat]

I haven't taken Calculus in almost 13 years, but I still watch Patrick's videos to keep me in check. I must soon make a donation to this fine, young man. And since the last example is pi over 4, is it possible that I could have a piece of that pi?

[mini1028]

I am not taking calculus anymore but I'm still watching your videos because they're so interesting and awesome!