I love how much reduction and simplification you have to get to sin^2

Thank you very much. I had a very similar problem but just different numbers. Take care!

After that long integral imagine forgetting + C.

@arjunsinha4015

3 жыл бұрын

Yes

@garydan

Ай бұрын

The teacher: minus 5 points for forgetting +C

There is an exercise involving right triangle wich helps derive u subsitution for these integrals

this is what im looking for. thank you soooo much

@blackpenredpen

7 жыл бұрын

you're welcome

YOU SAVED MY LIFE THANK YOU

You are awesome!!!!!! well done all around.

Thank you so much. I was super confused on the part where we change from theta to x again and inserting it back into the function.

Hey ! I've been watching your videos for a while, but I still cannot find in my books the inverse function of the sec x, what is it exactly?

you are the best!!!!!!

Can you help me with the exercise #19, sect 7.3? please thanks for the video :3

Can you do a video on a Integral Problem for sqrt(9-x^2)/x^3

Subscribed ! thanks a lot !

thank´s, it help me so much

saved my day!

The only reason I could do this is because of you, dr peyam, flammable maths and fematika (although he does higher level maths) Thank you sooooo much!

Been doing trig sub as an adult who's teaching himself for fun. I got this right first Try. Time to learn application of integrals!

Thank you so much !!!

i got stuck after sin^2(x) thank you :D you are the major reason why I know trigonometry substitution :D

Gracias eres increíble 💕😊

Thank you so much

can +you please make a video of x=a.sec θ and show on the triangle please?

Thank you!!

thank you very much!!

THANKS A LOT.

can you do sqrt(x^2-16)dx

thanks for all the help!

Thanks sir ❤

Hey, you put a 9 after removing aswelll

thank you bro

Thank you sir so much

I knew how to do this yay!

Thank you Mr math guy!!!

Thanks

I need to do reciprocal of this but 9-x²

thx

Hey BPRP! Is it true that you prefer to use integration by parts now to integrate sin^2(theta) when using trigsubs?

He has no idea what he is doing, the ball knows alll!

@blackpenredpen

8 жыл бұрын

Yup. The ball is my spirit!

@AlchemistOfNirnroot

8 жыл бұрын

+blackpenredpen I'm doing A Level Maths. We do U-Substitution but this trig for algebra substitution looks more advanced and the reasoning isn't known to me. Why can't you do U=x^2-9?

@johnsondirtbikes9346

8 жыл бұрын

+AlchemistOfNirnroot. if you use u=x^2-9 then du would be 2x and you wouldnt be able to plug in du because it has a variable in it

@AlchemistOfNirnroot

8 жыл бұрын

JohnsonDirtBikes Oh, thanks.

@nathanwright7775

7 жыл бұрын

You can still plug in du for dx, you just have to solve the equation for x and plug in into the equation

*Nobody* : *Integration* *is* *difficult* . *Blackpenredpen* : *Hold* *my* *pens* .

Thank you so much! Your videos are great to check where I've gone wrong when I get stuck.

@blackpenredpen

5 жыл бұрын

Yay!!

@alexkaranja9981

5 жыл бұрын

@@blackpenredpen try this one out...integral of 20x(x^3+3)^9

@ernestschoenmakers8181

3 жыл бұрын

@@alexkaranja9981 Just expand the integrand and then do the integration, it's gonna be a very long answer.

WHAT A MAN

Fantastic proof, but there could a little inaccuracy. First of all, the domain of the function f(x) in the integral is D = {x=3} In D, f(x) is positive when x is positive, negative when x is negative. In the "teta world", sqrt(tan^2(teta)) = |tan(teta)|, so your solution is correct if and only if tan (teta) = tan(arcsec(x/3)) is >=0, and this happens if and only if x>=3. So, the correct solution of the integral is your solution multiplicated by sgn (x).

You need to change your name of youtube to blackpenredpenbluepen hahaha thanks for u teach time!! u help to me so much sorry for my bad english :P

Thank U🥺❤️. MX

+AlchemistOfNirnroot When you let u = (X^2-9) and take the derivative, you get (du/2)=xdx which doesn't show up in your numerator so it doesn't help simplify things because you can't integrate x with respect to u. Hope that's helpful, I am no expert!

@Dav.02

Жыл бұрын

You will get to integral (u/x^3)(u/x) du

Can you solve the same problem?the only diffrence is sqrt 9-x^2 and instead of x^3 only x?

@ernestschoenmakers8181

5 жыл бұрын

Well if you let x=3sin(u) where u=arcsin(x/3) and dx=3cos(u)du then after doing all the steps for solving the integral you'll get I=sqrt(3-x^2) + 3lnIx/(3+sqrt(3-x^2)I + C.

good work but can you see me integral with suite

how did sin^2 teta turn into 1/2 (1-cos 2teta)?

@tommyliu7020

10 ай бұрын

That’s a formula you memorize

absolutely bonkers problem

How did he get value of dx?

@AbiRizky

7 жыл бұрын

since dx is the derivative of x, and x equals to sec(u), then dx equals to the derivative of sec(u), which is d/du (sec(u)) = sec(u)tan(u), which means that dx = sec(u)tan(u)du. Sorry for using u, don't have a key for theta

why are we allowed to omit the absolute value when we take the square root of tan squared theta?

@crosisbh1451

5 жыл бұрын

i think it might be that the square root is only positive while talking about functions. Don't quote me on that though.

wait but i thought 1-2cos(2x) = (sin^2(x))^2 not sin^2(x)

great great

Hello how are you?

why not √(secθ)^2-1 = | tanθ | abs.

how to integrate x^3(√ 4-x^2)dx

@herbcruz4697

5 жыл бұрын

Break the x^3 up as x^2*x, and then let u = 4-x^2. That's your hint.

It really shows that you NEED to know all the trigonometric identities

in the final answer why did you write sec^-1 but not sin^-1 cos^-1 ?

@immutabledestiny6377

7 жыл бұрын

Lai Linder , the reason for this is when we perform this substitution, we use x=3sec(theta), because of this relationship, theta is given as the arcsec(x/3). The reason arccos and arc sin are used is that they define a relationship in theta, and the original integral is with respect to x and not theta

@immutabledestiny6377

7 жыл бұрын

Are not*

@Ravenspeed

7 жыл бұрын

+Andreus Brammer thanks, I've successfully passed my calculus 2 course and this all makes sense. Practice makes perfect : )

absolute god, thank you. Brilliant teacher

Επειδή ο εκθέτης του χ ( που είναι εκτός της ρίζας) είναι περιττός δεν χρειάζεται η τριγωνομετρική αντικατάσταση. Απλώς αντικαθιστούμε την ρίζα ίσον u !!! Όσο αφορα το χ στον παρονομαστή, απλώς πολλαπλασιάζουμε πάνω και κάτω επί χ!!!

I’d have done it differently I’d have either used 3 cos x or 3 sin x

your answer is correct if tan(theta)>0 but false when tan(theta)

Why not just use theta = sec^-1(x/3) in place of sin(2theta), in other words, just plug in theta inside the sin(2theta)?

@harrywang2795

5 ай бұрын

You can and there’s nothing wrong with that, but sin(2(sec^-1/(x/3))) looks much more intimidating than the answer he got, if you can simplify your answer you should

@gingermuro6388

5 ай бұрын

@@harrywang2795if that expression (sin(2*sec^-1(x/3))) were to have the limit as x approaches infinity, do you know what the answer would be?

@harrywang2795

5 ай бұрын

@@gingermuro6388I’m not sure, sorry

@gingermuro6388

5 ай бұрын

@@harrywang2795 it’s okay lol, i’m just stuck on a problem, but thanks anyways!

@harrywang2795

5 ай бұрын

@@gingermuro6388 No problem!

The thumbnail said “dt” but is in terms of x

dx , but not dt in title

gracias por la explicacion amigo, saludos desde venezuela. El idioma no es barrera para transmitir conocimientos

The term power reduction formula refers to the formula which you derived in the video kzread.info/dash/bejne/q2Fty7SJdbG-n7g.html and using it in this context is confusing

You can avoid trigonometric functions here First calculate by parts D I + sqrt(x^2-9) 1/x^3 - x/sqrt(x^2-9) -1/2*1/x^2 -1/2sqrt(x^2-9)/x^2 +1/2Int(x/sqrt(x^2-9)*1/x^2,x) Let u = sqrt(x^2-9) u^2 = x^2-9 2udu = 2xdx udu = xdx x^2=u^2+9 -1/2sqrt(x^2-9)/x^2 +1/2Int(u/u*1/(u^2+9),u) -1/2sqrt(x^2-9)/x^2 +1/2*1/3*Int(1/3/(1+(u/3)^2),x) -1/2sqrt(x^2-9)/x^2 +1/6arctan(u/3) -1/2sqrt(x^2-9)/x^2 +1/6arctan(sqrt(x^2-9)/3)+C

NYC qst

the thumbnail says dt; you just put a t in the numerator

@blackpenredpen

3 жыл бұрын

Ah, that’s a mistake.

You used a blue pen.

dx not dt

I would integrate this by parts and then substitute for square root

@AbiRizky

7 жыл бұрын

eh, isn't that kinda too much work?

The answer given is incorrect when x 0, SGN(x) = -1, if x < 0, SNG(0) = 0.

So I'm on top of my game now? I haven't even started my calculus 1 course....

He is so young here lol

Ojala hablaras español

@ang_gml

5 жыл бұрын

No es un inglés muy complicado, además, si pones atención a lo que hace en cuanto a la parte matemática, podría hablar en cualquier idioma y no habría problema alguno.

Kinez zadao alo care gore oznaciiiiii.

You need to work on your pronunciation

@JennaLuuLuu

3 жыл бұрын

unnecessary comment, clearly English is not his first language, however he is still trying and helping us learn. He is doing something for us (which he doesn't have to do) and you are being offensive.