Integral with sqrt(a^2-x^2) -- inverse trig function needed

[yingmujielun]

so what if a is not equal to 1?

[saad095]

if it was possible to integrate this equation without using da substitution method then one could have got the value of pi by integrating this circle equation between 1 and -1 Hell pi and e always create a fuss

[dsilvestre]

Isn't Sqrt(1-sin^2(t)) = |cos(t)| ?

(Observe the absolute value)

I don't understand why he simply says it equales cos(t)

(It's in the middle of the whiteboard)

[yquechula]

I thought this video was great! I'm taking this for the first time in class, (I'm NOT adanced at all) and the Prof just flew right through it because it was "so easy". Thanks for posting all the different views of the problem, it was SO clear.

[dauzz92]

thanx a lots 4 dis video..its really help me.

[badadelgbrian]

Also this video has too many views for this simple problem.... i the reason why i am angry is because he introduces the problem to youTubers as if it were difficult by saying " THAT LOOKS PRETTY TOUGH , I'M NOT SURE HOW TO START WITH THAT....... BUT WE'VE GOT A RECOMMENDATION" -- seriously... i mean seriously???

[mesmicdav]

I am trying to post you one calculus problem, but cannot send thru here, any other way I can post you this maths problem??

[mesmicdav]

Thanks for your video,is very helpful

[Reloadedrhapsody]

Thank you Midnighttutor you really helped me! I knew the solution to the integral, but I didn't know how to get to that solution.

[xpreshuzz]

wowwww its midnight when i'm watching this right now. def useful tho. calc ab ftw.

[Asterog3624]

Enter this in Wolfram Mathematica: "Integrate[1/Sqrt[1 - x^2], x]", get result.

Enter ANYTHING in Wolfram Mathematica, get result.

[rhk01]

you guys are all nerds lol :P

[olliehouse9]

integrate 1/sqt(a^2-x^2) = arcsin(x/a) + c

its in the formulae booklet lol :P

[emilioelchingon]

lol it's exactly midnight when i watch this video

[Chrisoutwright]

assuming a is not 1, how to go about it? there's no identity now fitting this easily as before.

[TheDeskuuul]

clear and precise... keep it up

[MONKFOCKER]

integrate(x^2)/(1-x^6)

integrate (dx)/squareroot(4x^2+16)

integrate (dx)/(x+1)squareroot(x^2+2x)

[apcharding]

fantastic explanation. very clear and thorough.

[guitardude1243]

Most excellent, I completely forgot about Trigonometric Substitution, would make some of these Iterated Integration problems much easier.

[icafemoto]

why do i get the integral as -arccos(x) when I substitute (1-x^2)^(1/2) = sin(y) ??

[icafemoto]

NEVERMIND, i think i figured it out myself.

After solving for C, -arccos(x) + C = arcsin(x)

C = pi/2

[gnatz182]

This video is excellent, wonderfully explained.

To those people who say that just by looking at it you can tell that it's arcsin, yes, that is true, but knowing it as a recognition rule and not a solid derivation is useless.

[badadelgbrian]

@gnatz182 useless??? are u serious?? is like saying that in order for you to understand how you got 4 from 2 plus 2, you will need to count each one of your finger to get four.... instead of learning that by fact,, not because of recognition.... that is why they call it formula.. because it works no matter what!

[gnatz182]

@badadelgbrian yes, I'm serious. And isn't that how you learned to count? Just because you know how to count quickly now, doesn't mean it didn't take some solid learning. I'm not saying you always need to derive everything, but bearing in mind how your maths is working is a useful skill. What happens if you're in an exam, look at an integral, and can't remember its 'rule'? If you only learned the rule, you'll be stuck. If you learned the derivation, you're home free. :)

[badadelgbrian]

@gnatz182 i totally agree with you ...... but don't discourage people by saying that the problem was hard. ur video is good but ur introduction was not optimistic or realistic.

[golomov]

great job man, couldn't have been better.

I wish I had a teacher like you.

well done

[PPJens]

explained perfectly! well done!

[ccsingle07]

Helpful, sort of, except the constant head turning is very distracting

[korrisha]

I have 2 question please help help. Find the integral of (1) inverse (4 + x^2) sqrt or dx/ square root(4 + x^2) and question (2) dx/ square root(1 + 9x^2)

[seva809]

many thanks

[Waranle]

Give the man a break, ok there are people who dont even know what the arcsin means

[virajpala]

oi u gai boi dont u hav manners or wht ???? u should be thankful to the man.

[aesrp]

lol try to insult them and you're only wasting your own time hunterbender he probably does know that he's just going through other methods of solving the problem don't think your so smart because you do know it's quickest method of solveation.

[ratofirniliev]

Actually, its not "another" method. Its a "proof" of how the arcsine fuction is tabuled.

[bigDeeOT]

In most situations it's very good to know multiple ways to do it. But come on, this is seriously a waste of time. This problem is a DIRECT simple integration. It's exactly a one step problem. Doing ANYTHING else is a waste of time.

[hunterbender]

Isn't that arcsin function? You should know it in a glance, let alone spending 4 min + solving it.

[dziewuliz]

yup, that's arcsin...

[bkjoelover]

pwned becuz this guy doesnt know his inverse trig tables.