Integral of (sinx)^4cosxdx

[xxcowslayerxxx]

now take the integral of sin^4(x) without cos(x) next to it and post a vid for me

[rhobz2792]

ala kang kayapan nimal!

[colinwar]

very much a helpful video, thank you very much.

[bmthnumber1]

There's actually a formula wich is easier to use in that case (and similars).

It's: f(x) * f ' (x) = f(x)^n+1 / n+1

In words: When you got a function wich is a product, in wich one of its terms happens to be the derivative of the other term, then, the integral solution will be the f(x) to the n+1 power (being n its actual power (4 in this case) ), divided by n+1.

We re-write the integral as I: sin(x)^4 * cos(x) dx

The derivative of sin(x) is cos(x). Aply the form: sin^5(x) / 5 + c

Solved.

[bmthnumber1]

@bmthnumber1 I'm sorry, at the end of my commentary I should have said: "The derivative of (sin(x))^4 (the term inside the parenthesis only -sinx-) is cos(x). Then, the criteria for using the formula is valid."

[IvanGangsta1]

hahahahahahahahahahahahahahaha­ha

[Yu2Kal]

Wow, why are people being so negative, we are all human we make mistakes and learn from them, this guy is doing us a favour by providing helpful videos, if you don't like these then just leave the video and don't leave negative feedback, ungrateful people...

[kinghustla187]

NERD

[birandkoray]

really great idiot :D

[random19911004]

the guy on the camera knows more than him

[chris5903]

he just show the common mistakes like that.. hehehe

[wristrule]

Lol, he's teaching calculus, but doesn't know what he's doing? du/dx = cos x dx?

[netnplay]

Ummm...wait..isn't the derivative of sinx=-cosxdx?

[MPV839]

yup.

[MPV839]

i lied - derivative of sinx = cosx derivative of cosx = -sinx (opposite for anti-derivatives)

[flipponzin24]

Nicely done. Keep it up.

[nitish971]

d/dx however is an operator representing the derivative of a function of a variable "x".

[nitish971]

VERY IMPORTANT:-

"du" and "dx" are separate entities called "Differentials",.....so you CAN treat du/dx as the ratio of two numbers.

If u=f(x) is a differentiable function of x,

then du can be defined as du = f'(x)*dx.

If Simultaneously "u" is a function of another variable "y", then du = g'(y)*dy.

Considerable work is needed to show that these two definitions coincide.

[ImaginaryHuman072889]

lol i love when he hits the microphone and whispers, "i didn't mean to do that"

[juggy2008]

hold up, did I do this right? LOL

[haril007]

SUPER EASY lol

this is like a basic u sub. problem (by the way I haven't seen the whole video at all yet)

[pasa6006]

dayı süper analatıon yaw:)

[sh0cker13]

i love substitution

[csikjarudi]

integrate (f^n)*f' = (f^(n+1))/n+1

Anyway you cannot consider the du/dx as a fraction, use the substitution integral formula:

integrate f(x) dx = integrate f(g(t))*g'(t) dt.

[BBoyA2A]

du/dx is a fraction... cant believe im posting this on youtube... but yeah... what he did is correct... execept when he wrote 2 times dx lol, good day

[csikjarudi]

The facts: "u" is a _function_, and u(x) is the value of the function at point "x". So you can write u' as a derivative of function "u" for instance u=sin, u'=cos; u=id, u'=1; or you can write u'(x) or du(x)/dx, which means the _value_ of the derivative function u -- ie. u' -- at point 'x', 4example: u(x)=sin(x), u'(x)=cos(x); u(x)=x, u'(x)=1. So u' is a function and u'(x) is a number, needless to say there's a significant difference. So what about the du/dx, well it's meaningless.

[BBoyA2A]

dude have u ever studied math ??? du/dx means u derivate the function u by its variable x

its just a lineair operation. just think about partial derivation. ex if u do.. (dy/dx)*(dx/du)=(dy/du) now dont tell me that this isnt correct. nwayz, im not gonna argue anymore on this. have a nice day

[csikjarudi]

Ok. d/dx can be an operator indeed, but not a fraction and we talk about analysis of real valed function, not operators anyway.

Furthermore 16/64=1/4, but not because of you can simplify the number 6. Correct answer, but not in the correct way.

I don't think we argue. You're right, but the analysis what you talk about is not correct theorytically, but correct formally. And we all know that the formal things are just secondary importance for the deep understanding.

Have a nice day buddy.

[gamesguru]

Look at 1:30 to 1:40...he got owned. "Times the derivative of what's inside, dx". More like times the derivative of what's inside, 1.

[SuperBrilliance]

You always choose the easy ones.

[aswin1205]

Wait, that answer is incorrect.

Its supposed to be - (sinx)^5 / 5 + C.

[terminaterjohn]

no it isnt

[HappyCamper691]

where did you get the negative sign lol

[deathwishtomax]

This is not a "rather complicated" integral. It is very simple. It looks like you had a bit of trouble with it yourself professor. lol

[haril007]

lol ownage

[89tommyeflight89]

How would you find the constant of integration if it were a definite integral??? (he said you coould in the video) I understood that the constant is unknown, an arbitrary value if you will.

Also, this question is way too easy.

Try finding the integral of

(x^2)/{(3+4x-4x^2)^3/2}

It took me 2 substutions and more than 20 lines of algebra....

[operationcwal789789]

Do a Laplace transformation, solve it in time space, and do an inverse Laplace transformation. :-)

[gantz339]

Gracias me has ayudado mucho i like this video

[FlippinPin0y]

wow, integrals are like easy now

[zim01001]

I found this helpful, free teaching should be valued, great stuff!

[ligpgf]

well i am 18 years old... In Greece we study integrals in the 3rd class of highschool, and i find that quite easy...

[Lordbestami]

hi! I have a question... Does anybody know how to find that stuff: you rotate a funktion from y-line and you rotate that volume from x-line again. What is the volume in the end???

[11hani11]

what do you mean you think its easy... it is child's play...

[bkjoelover]

cheapass did not record in stereo mode again.

[hanshv]

I am Calculus College Teacher And I am only 22 years old , I think that this calculus is quite easy.

[TheOnlyTyrael]

Well, of course you think it's easy. Read the sentence you just wrote. -.-'

I'm only two months into Calculus, and I'm loving it so far. Keep up the good work, guys. =P

[bkjoelover]

lol his ass got pwned at 1:35.

[ultranordic]

Yeah, that was weird. I'd redo it before uploading. :p

[seyedseyedi]

this guy is an idiot

[Aloosh12]

hmm i never thought of that i was like maybe you can split the power 4 to sin^2 times sin^2 ----> then sin^2=1-cos^2...

[xlynnduh]

that's mathematically wrong.

[badfutureuk]

Look at this guy's awesome handwriting

[sweatshopboy]

u coulda explained the +C part-- u add +C becuase C is a variable standing for any number, in this case, because you are taking the indef. integral of the function, u do not know if there is a coefficient next to the x^0 power- which is C

[macchonk007]

it's easy....

[RedBrain812]

yeah man its so easy heh i remember back in the day learning that at high school going whaaaa lmao :P i love doing a degree in mathematics :D

[Vaeth13]

Have u even finished school.. n00b

[mturewicz]

lol so true mate, though he's trying, so gotta give it to him

[zaith88]

gd job..

[haquearsh1]

wow...

[Melan07]

EASY!!!!!!

[nosotrosde]

this is too easy:D

[nas2k44]

i failed my first pre-calc test cuz i cant understand my dumb instructor, but this is good. Youtube math rocks!!

[nas2k44]

Im learning math on youtube from now on, can't understand my stupid instructor anyways. I failed my first pre-calculus test, imma watch youtube and study. Area under the curve seems easy..but this, give me a week

[Differentiated]

sad, he's making it way too complicated

[PhilipGreen666]

Here's an easier way.

1)Take the sin/cos forget for the moment what is in the bracket, and find the integral.

2)what you have just found by what is differentiated inside the bracket.

3) put +C at the end!

[PhilipGreen666]

Far, FAR over complicated!!

[speedytheturtles]

awesome, I understood his teachings

[ssnatcherss]

integrate e^(-x^2)

[praky23k]

it's sqrt of pi

[barca7jr4]

lol that guy isn't very good integrating ... He put two dx in the same equation! but nice teaching though, its obvious that he is a highschool teacher .

[drcroc2]

uhhh, he just did that perfectly, and neatly. what are you talking about?

he should do more interesting problems tho, this is too easy.

[olgis]

AMAZING!

[b0000b]

dont want to learn on youtube.