Trigonometric Integrals - Part 3 of 6

[Axloooo]

Do we really need to learn all the so-called formulas you're showing us at the beginning of the video? how am I supposed to know which one to use and learn all of them by heart

[SN1P3ALLSN1P3RS]

I have a test tomorrow on all this stuff, I watched a few of your videos and went from a confidence level of 0 to a confidence level of 100, thank you so much!

[kkkasha01]

thanks to you i will pass college

[patrickJMT]

@kkkasha01 ha! hang in there

[laurenclark31]

I'm struggling in Calculus II and find your videos very helpful. Thanks. Why do I get a different answer when I do a u substitution with the same things but at 4:01?

[ICarnag3I]

your integrals become more like "S" as the video progresses = ]

[Cowboys2SB]

Thanks Patrick, your the type of people that make a real difference in the world. Great job mate.

[patrickJMT]

@Cowboys2SB just doin' what i can

[HouseMuzik4Life93]

How come in the first problem you only used the trig identity once? And why the middle function? Is there a specific reason for these things? Thank You

[Mogon11]

When you reach reach the integral of (1+tan^2 x)(sec^2 x) at 3:59 could you take u=tanx and then get integral of (1 + u^2)du?

[Barbarian74]

@IWANTHOTDOG Actually... thats a real good idea...

[lilhud100]

In the last example doesnt the u subsitution suppose to be tan^2x instead of tanx?

[robdog979]

This might be a dumb question, but at 4:00

Why cant you just take u of tan^2 x and get its du cancel out with the sec^2 x term?

[ronniemonnie]

@robdog979 because the derivative of tan^2(x) is 2sec^2(x)tan(x)

[lobsidedballs]

Can you do integral of Cos^4xdx?

[AnDyCls]

GRACIAS ME AYUDÓ BASTANTE=D

[JaoquinQ]

What about products of cos^2x and tan^3x?

[Ayplus]

@IWANTHOTDOG If only physics was this simple

[ballermanz]

I'ma have my test on thursday... x.x~~~ on all integral stufff.. wish me luck :D

Your videos are very helpful, cover most questions and the course.

Is it k to make requests for problems in case i have trouble wtih them?

[tacopeut]

I bet at 5:15 you felt clever writing out that u with parenthesis and and underscore.

[NeoXC]

Can you do something like integral [(cosx)^6][(sinx)^6]dx? I'm being asked this on a practice exam, and I realize there's power reduction formulas out there...but in all honesty, how would I be able to memorize every single power reduced form for cosx or sinx (greater than powers of 2)? Is there a systematic way to do this?

[NeoXC]

@NeoXC Oops, I meant to say the integral [(cosx)^6 - (sinx)^6]dx

[towch1]

cheers from UMBC!!!!...ur the best

[PhotoshopBro]

Simply, you are the best Patrick! I got a full mark in the Calculus II quiz because of your videos! :D

[patrickJMT]

@PhotoshopBro congrats : )

[hassancheetah]

Mr Patrick I want to make some correction in your solution and it is that if you had substituted tan x with u in the 3rd step to make it (1-u^2). and then substitute dU in place of sec^2 dx. It would be much easier. Anyways, your videos are helpful and I want to thank you for that.

[patrickJMT]

@hassancheetah you are probably right, i take the scenic route on a couple of problems!

[1matth3w1]

@patrickJMT he is actually right right on the 3rd step you could have just used u substitution lol since a sec^2x is present . execellent videos as always lol

[dj2can]

@hassancheetah I was thinking the same thing. LOL Makes it easy, but then again, new ideas aint bad for ya ;)

[mzzchunsa]

omg so helpful! thank u so much!

[2Luke]

thank you sooo much! holy crap i was stuck on this problem for ages!

[Cybernetic]

@IWANTHOTDOG agreed man, physics is killing me right now haha

[shamzahm]

thank you.

[MomosReel]

Calculus is fun.

[teasonmeow]

well done again, thank you, ur a lefty homie

[hkpopfan4lif3]

yeah i just did (1+tan^2x)sec^2x dx = integral of (1+u^2)du

=u + (1/3)u^3 + C. easier

BUT, when i went on wolframalpha and typed this problem in...it gave a totally different answer. It used the reduction formula...can anyone tell me why that is?

[Shenzinator]

@hkpopfan4lif3 Yeah I was wondering why he didnt stop there.

[kashiark]

errr du=sec²(x) dx

[kashiark]

for the second problem, you could just set u=tan(x) and du=sec²(x) seems easier

[Physicsandmaths]

I've got my other original sec² hanging out there... just chillin' out.

It's so funny :P

[fandennis]

wouldn't it have been easier just to leave the (1+tan^2x) unexpanded and did a u substitution from there (1+u^2)du and integrate? (saves one step) 5stars JMT!

[DiscoOnRocks]

I don't think that would have worked because you need to isolate you sec²x in order to define the problem in terms of u. By letting u immediately your sec²x is still attached to the equation. You may get the same answer but it is mathematically incorrect.

[mitchyd89]

I'm not sure what you mean. It is just like the other problem he did.

int (1+tan^2x)sec^2x dx = int (1+u^2)du =

u+u^3/3 +C. It checks out.

[mitchyd89]

I meant to reply to discoOnRocks but it put it up here...idky

[sjb167]

Yea that works, i did in my head while he was doing it the other way. So yea you could skin a cat in more than one way lol

[ElBrillante4]

thanks man.

[calvinhobbesliker2]

how do you integrate a product of sines and tangents?

[delhigod]

I'd guess break the tan into sin/cos and work from there. I'd go with u substitution.

[dreamonlittleman]

in step 3 why did u distribute? can't u just let u=tanx du=sec^2x and then it would give

u (u^2+1) du to integrate ??? i dont understand why substitution is necessary

[dreamonlittleman]

give u*  you

[sakibalmahmud]

can u find the int of sin^6

[patrickJMT]

it would be very tedious! you would have to write it (sin^2)^3 use identity, expand, and use the identity some more!

[julesickdrums]

@patrickJMT

oh please do: sin^6+tan^8, c'mon one time pleeeeeeeeeaaaase?? (O)_(O)'

[ozakigw]

There's a quick fix formula for these type of integrals

1. Int(cos^n(x)sin(x) dx) = -cos^(n+1)/(n+1) +C

2. Int(sin^n(x)cos(x) dx) = sin^(n+1)/(n+1) +C

3. Int(tan^n(x)sec^2(x) dx) = tan(n+1)/(n+1) +C

These are just some rules i picked up from my high school teacher to make life easier during exams.

[goosefrabbas]

Before you distributed the sec(x) a little after the 4 minute mark.

[MATHGEEK1989]

Why didn't you just let u=tanx in the third step, and the derivative of tanx would be (secx)^2 which we have. And the answer would be x + (tanx)^3/3??

[patrickJMT]

i did let u = tan(x), right? i am confused... not sure where the problem is...

[EatShanklish]

@patrickJMT I think what he means is to use the U- sub method before you distributed the sec^2 onto the (1+tan^2). So u=tanx, du= sec^2, so S (1+u^2)(du), then integrate to get U^3/3 then swtich it back to Tan^3/3.

[patrickJMT]

no, cause u = tan(x) so u get the same answer i got : )

[DMAlivenow]

i agree with mathgeek, but either way works. Recognizing patterns and which roads to take is a very valuable skill in mathematics.

[ultimaweap12]

@MATHGEEK1989 I get what u mean. I also did it this way. I didn't multiply out (1+(tan x)^2) with (sec x)^2 before letting u=tanx and it also gives me x+ 1/3*(tan x)^3... I'm guessing your method is correct but i'm a bit confused as well...

[jay2yosi]

@MATHGEEK1989 I thought that the answer for this questions is x + tan^3/3 though, unless geometrically or algebrically are the same answer with your results in the video. Any way as always u are superp online teacher !