Integral of sin^3(x) by trig identity and u-substitution. This is a calculus 2 integral. For more calculus tutorials, check out my new channel @just calculus 👉 / justcalculus
Sin3x=3sinx - 4sin^3x From this formula , Sin^3x=3sinx-sin3x/4 Now we can easily integrate by taking 1/4 outside and giving integral sign to both of them ...🙂
Yes you are completely right but no one ever remembers this formula (at least i never remembered it) though they know about it.What we saw in the video was more "practical" nevertheless whatever people are comfortable with should be used.
Thank you, Asian Ball Man. You've not only helped me remember a missing fragment of the nightmare that was calc II, but you've also taught me to love. To love with the power of the ball.
[yet another "thank-you" comment] Got here after not understanding the steps my teacher followed to reach the final answer. Awesome video and awesome, super clear explanation. Thanks a lot :)
I always like videos like this. Furthermore, the video made the process easy to understand. I know this would be a slightly different way of going about solving the integral, but would it not be simpler, using u-substitution, to manipulate du into equaling sinxdx? This would result in -du, which could be plugged back into the integral, then the negative of du (-1 constant) could be brought to the front of the integral.
I just learnt complex numbers and cams back to look at this vid. Ah how beautiful to see the times where I struggled with integration of weird trigo functions, now with complex numbers it’s almost like cheating.
Helpful, I start to forget the most basic trig the higher I go... was trying to use the sin^2x=1/2(1-cos2x) for some reason and thats why I couldn't get it...
That is lovely. Thank you I feel so daft, 60 years too late to find it all making senseMight as well make this my bucket list... learn another integral....might even try to do some myself before looking to you for the answer.
yeah it was really great but is the thing in your hand for translating to english or for recording sound . but i really enjoyed the video so much even subscribed already and also hit the 👍👍👍👍👍👍👍👍👍👍👍👍👍✔
2:14 I was taught that we can't integrate trigonometric functions in the same way as polynomial functions though. Does that change when we integrate by substitution? If yes then why can't we integrate it directly?
mesmerised by your pen switching sleight of hand
This comment made my day!!!
+blackpenredpen i strongly sympathise with this comment. and with your sleight of hand. pens for the win!
+Daniel Walther Thank you, thank you~
btw, there's a video on that th-cam.com/video/akYITCn0Ecg/w-d-xo.html
Oooo i see...... ❤
Alternative:
Use : sin3x=3sinx-4sin³x
sin³x=(3sinx-sin3x)/4
∫ sin³x dx = ∫ (3sinx-sin3x)/4
on integrating = -(3cosx/4)+cos3x/12
👍
But The Answers Are Completely Different How??
@@raghav9o9 Substitute cos3x =4cos³x - 3cosx. Will be getting the same answer.
So i am confused can't we use formula of
Cos2x=1-2sin²x
sin²x =1-cos2x/2
This is exactly what I was done
In the U world
I appreciate you and your microphone immensely :)
david112755 lol. Thank you
I like how this is 3:14
+Dan Dart 3,14159265358979
+Dan Dart edit:3.1415926535897932384626432795028841971
+a pool player that's wrong after 4626, it goes 46264338327950288419716939937510
Taking it up another step 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899
3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049 951059731732816096318595024459455346908302642522308253344685035261931188171010 003137838752886587533208381420617177669147303598253490428755468731159562863882 353787593751957781857780532171226806613001927876611195909216420198938095257201 065485863278865936153381827968230301952035301852968995773622599413891249721775 283479131515574857242454150695950829533116861727855889075098381754637464939319 25506040
All my classes are online now because of the coronavirus, but these videos are saving me. Thank you bprp 🙏
Great explanation! I could never figure out how to where the negative sign came from. Thanks for the awesome break down!
Awesome video. But why are you talking into your shower head?
diamondsmasher ㅋㅋㅋlaughing out loud
lol
Omg. That's the first integral from your channel I solved by myself. Your videos are excellent!
Explanation was crystal clear.....
The way switch the colour of the marker is just cool
I'm actually finishing my bachelor engineering, sometimes we forget, but with your video I was back on track, thanks a lot !
THANK YOU, i have a midterm tmr, and I did not understood substitution properly with trig. This was very helpful!
Thanks, that was a great refresher.
these all really really help me to understand what's the correct way. thankiee!
sir , you teach so smooth and so clear .
The pen switching was lit! Thanks so much!
this one save me so Thank you. I was so clueless about the lesson our instructor send us but through this, now it make sense.
Sin3x=3sinx - 4sin^3x
From this formula ,
Sin^3x=3sinx-sin3x/4
Now we can easily integrate by taking 1/4 outside and giving integral sign to both of them ...🙂
Yes
Yes you are completely right but no one ever remembers this formula (at least i never remembered it) though they know about it.What we saw in the video was more "practical" nevertheless whatever people are comfortable with should be used.
So i am confused can't we use formula of
Cos2x=1-2sin²x
sin²x =1-cos2x/2
even after taking diff eq and getting past fourier transforms and stuff after that. i still forget things. thank you mate
Superb tutorial. Thanks a lot man!
Thank you, Asian Ball Man. You've not only helped me remember a missing fragment of the nightmare that was calc II, but you've also taught me to love. To love with the power of the ball.
muchas gracias hermano , me suscribo de una . Explicas demasiado bien las integrales
I love how this video's length is the value of π
you're brilliant
Thanks a lot i've bees searching for one hour this ^^
i like math... seemed more interesting than the rest showing up on youtube.
this is what i call entertainment while being ill!
Math is fun!
+blackpenredpen yup
Wis I felt the same way :(
@@blackpenredpen ya
Danke dir fur es.
Fantastisch!
You make it look easy. Thanks.
[yet another "thank-you" comment]
Got here after not understanding the steps my teacher followed to reach the final answer. Awesome video and awesome, super clear explanation. Thanks a lot :)
You used substitution method nicely.no matter what are you using it matters how are you solving.very great substitution and 5 🌟 for adjusting. By
Awesome explanation, thank you!
Awesome video :) , suscribed!
my o levels are in like few months, and i gotta say, this is actually really helpful bro, thanks for the sweet vid dude
Thanks. This was really helpful!
I always like videos like this. Furthermore, the video made the process easy to understand. I know this would be a slightly different way of going about solving the integral, but would it not be simpler, using u-substitution, to manipulate du into equaling sinxdx? This would result in -du, which could be plugged back into the integral, then the negative of du (-1 constant) could be brought to the front of the integral.
Very well explained, thank you
Thanks for solving doubt
You are really amazing sir. jazakallahu kair. May lord guide u on straight path
Wonderfully explained!! 😊😊
Really u r amazing good job 👏🏻
Thank you!! I was desperate and you helped me a lot!
glad to help!
thank you mate you saved my night
Thank you for saving my life. AGAIN!
Amazing work bro :)
Great job! Thanks a lot! Easy and vivid!
I am glad to help!!!
You could also use the formula sin^3x=(3sinx- sin3x)/4
Thankyou! It Helped me to cross check my answer
It works nicely by parts
wow you're amazing teacher thanks a lot
Thank You. Very well explained. :)
Gracias por la explicación. Are you does videos about series of potential?
your a great teacher! :)
I love you teaching method ,me from India
Excellent solution
omg this came up in my exam the other day
Thanks for allowing me to pass calc mate.
Very helpful! Thank you
THANK YOU SO MUCH FOR THIS; V HELPFUL
try doing it by coverting it in triple angle. sin3x=3sinx-4sin^3x
I just learnt complex numbers and cams back to look at this vid. Ah how beautiful to see the times where I struggled with integration of weird trigo functions, now with complex numbers it’s almost like cheating.
You look very different compared to now.
Helpful, I start to forget the most basic trig the higher I go... was trying to use the sin^2x=1/2(1-cos2x) for some reason and thats why I couldn't get it...
That is lovely. Thank you I feel so daft, 60 years too late to find it all making senseMight as well make this my bucket list... learn another integral....might even try to do some myself before looking to you for the answer.
wow that's great!!
I am so grateful for this
How to solve if it has double integration and two limits that are 0 to π and 0 to 2π
your video is great!
Can you do a video for Integral of x sin^3(x)
thank you very much!
Awesome explanation 🔥🔥🔥
U did it great but I really liked ur baowl
Can you do a video on solving the indefinite integral, from 0 to infinity, sin(x^2) dx or sin^2(x) dx ?
amazees me every time
Ur talking expressions are totally different from us...but instead of this...it's so helpful..🇮🇳🇮🇳🇮🇳
Thank you for your help
I understood everything even though I speak spanish. Thank you
Thank you, saved my homework.
"U" nailed this nicely, and I am a SUB. (:o)
+lexinaut Thank "U" too!! =D
Thanks man...It helped me...!!
Superb sir explained superbly
Thanks along my guy 👍🏾👍🏾
thanks me sirvió.. very good !!!
Your explanation is super to dupper thank you sir . I purple you 💜💜🤩🤩
LEAN
LEAN
very very helpful thanks :)
awesome dude!
Thank you.....😊😊☺
yeah it was really great but is the thing in your hand for translating to english or for recording sound . but i really enjoyed the video so much even subscribed already and also hit the 👍👍👍👍👍👍👍👍👍👍👍👍👍✔
Very good!!
who else was worried at -integral(1-u^2du) where it should be -integral((1-u^2)du)
seriously i spent 5 minutes trying to figure out how he just took out the parentheses!
Creative & Random also he forgot +constant after the integration, but then placed it after subbing cosx.
Meeeeeeee
sir ihave opinion that we can directly use du instead of -sinx dx and take the negative sign out of the integral
explained it better in 3 minutes than my AP AB Calc teacher did in 50
2:14 I was taught that we can't integrate trigonometric functions in the same way as polynomial functions though. Does that change when we integrate by substitution? If yes then why can't we integrate it directly?
Very plain explanation. Good job :)
Thank U!! You save me hahaha
Thanks a lot.
Awesome!
Thanks!
thank you so much
Thank you very much. Teacher
Sin3x=3sinx-sin^3x this formula can be used for integration....
comedy ka khazana sab ko hasana sin3x= 3sinx-4sin^3x
u r a bit wrong Gaurav
it should be sin^3(θ)={3sin(θ)−sin(3θ)}/4
Thank you sir
You are wonderful
Thank you sir
thank you!