Integration Using Inverse Trigonometric Functions - Ex 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!!

[koalabear]

it's because when you differentiate a function the constant goes away (it is zero). think d/dx of x^2+4 just becomes 2x. when you go in the opposite direction (the integral) there is no way of knowing if there was a constant in the original function so you tack on the arbitrary constant to account for it. basically it is saying each function has an infinite number of indefinite integrals.

[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!

[packer]

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.

[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?

[Gunnerz]

for peeps who are asking:

say u had 1/x^2+n, and u wanted to change it into the form inv.tan(x), u would do so by:



kinda hard to explain like this but hope it helpsss.!

[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.

[jlim]

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

[IrishPrid]

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

[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!

[shadybot]

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

[TheDrastic]

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

[matthewdcimino]

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

[andrewsr]

@patrickJMT minor mistake but the domain for the inverse of tanx is from -pi/2 to pi/2 non inclusive for both

[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

[MohamedSharif]

Patrick can you help me out with this question

integral of 1/(4+9x^2) i know this follows the rule where it's 1/a arctan(u/a) so just by looking at this i can tell that a=2 and u=3x so the answer should be
1/2 arctan (3x/2) but the answer in the book is telling me its 1/6 arctan (3x/2)

my question is how come it's 1/6 and not 1/2 when a=2?

[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

[patrickjmt]

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

[Mysteryp]

hello,
arctan(u) to definite 1 to 0 why we put arctan(1) - arctan(0) right away instead of putting U back to cosx?

[valeriediaz]

YOU ARE Thank you!!! You saved me from so much stress :')