integral of sin^2x*cos^2x, calculus 2

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integral of sin^2x*cos^2x,

blackpenredpen

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2:26 "I can say bye bye to the cos *big smile*" fantastic moment in mathematics

brianmiller

You are simply a genius .
No more words. 🥰🥰
Keep up with the good work
You have helped so many students and made calculus a bit easy for us

hs-eh

ちょうど解けなくて困ってましたありがとうございます！
Thank you ！！

さと-g

Is that a Supreme shirt that your wearing?

AaronQuitta

I solved it using the power reduction formula before watching the video:
sin^2(x)*cos^2(x) = (1/4)(1-cos(2x))*(1+cos(2x)) = (1/4)*(1 - cos^2(2x)) = (1/4)*(sin^2(2x)) = (1/8)*(1 - cos(4x))
Now, this is very easy to integrate: (1/8)*(x - sin(4x)/4) + C

Miaumiau

yaay I'm so happy today!!
This is the first time I solved a blackpen redpen question all by myself!!!

lerolerolerolerolero

i like you and your videos. Thank you for this. 👍 - Your Turkish follower

selingonul

Needed this as a way of solving the integral (x^2)(sqrt(16-(x^2))) with x interval [0, 4]. I was at 256 * integral (sin(x))^2*(cos(x))^2 before looking up this video.

joebop

I really like ur teaching style sir.
Ur student from 🇮🇳India🇮🇳

utkarshmishra

I am surprised I actually solved this question the exact same way you did!

aniketgupta

Thank you! You are very good at explaining :D

skrfreak

Thank you so much sir!! You make integral more understandable more power God bless.

irahraquinio

I am surprised that the method I have done by myself is the same as the one in the video. Proud to have fount the same trick avoiding complex exponential 😁

romain.guillaume

Thank you! Saved me from spending 24 hours on this problem

jonnypoland

Your videos are too good even your thumbnail helped me before video

Roronoa__

Was going over my summer homework and had no idea how to do this question, looks at this and had never seen that identity then realised i skipped a page in my work explaining i had to learn 2 new identities aghh

louissilsby

can you solve the integral of x*(arctanx)^2 in terms of x (dx)?
Thanks you, you are the best!

fkaspow

thanks! This is easier than the way I was approaching it!

ResidentTitan

hey you solved my doubts. i am from India and able to understand you. thank you

x_lofi_song

‏definite integral examples 1-(cosx)^2/(sinx)^2 the period ranges from -180 to 180

glaratalib

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This chapter closes now, for the next one to begin. 🥂✨.#iitbombay #convocation

Integral of sin^2x*cos(x) vs integral of sin^2(x)