Up late studying sin^2cos^4 and reading the work had me flabbergasted. Went to sleep, woke up & remembered my trusty online tutor. You absolutely rock. I watched this video and used your approach to solve mine with ease.
yes, i'm planning to do a couple more of these. i would expect problem where m =/= n would be quite long and tedious. all of these problems usually are. unfortunately, the quickest way i know to solve them is still just to simplify the odd identity. :)
in that case you just go straight to the half angle substitution, and substitute (1/2-1/2cos(2t)) for sin^2t. then you just integrate term by term. make sure that when you take the integral of cos(2t), you use chain rule and divide by the derivative of the inside function, 2t. then evaluate at your limits of integration. :)
Sine and cosine terms come up a lot in e.g. electrical engineering when AC currents are being dealt with. So it's not improbable that if you're working in such a field you'll meet one.
Rewrite trig function with sec(x) and tan(x) or cos(x) and sin(x) From Euler substitution we will get sec(x)=u-tan(x) for sec(x) and tan(x) version or cos(x)=(1-sin(x))u for cos(x) and sin(x) version
i did this for sin^2(x)cos^4(x) and got stuck when i end up with (1-cos(4t))(cos^2(t)) I dont know how to remove the cos^2(t). I know I can use 1/2(1+cos2t) but that doesnt make it any simpler, since i end up with cos4t and cos2t multplying, can anyone explain?
Up late studying sin^2cos^4 and reading the work had me flabbergasted. Went to sleep, woke up & remembered my trusty online tutor. You absolutely rock. I watched this video and used your approach to solve mine with ease.
Oh good! I'm so glad it helped! :)
yes, i'm planning to do a couple more of these. i would expect problem where m =/= n would be quite long and tedious. all of these problems usually are. unfortunately, the quickest way i know to solve them is still just to simplify the odd identity. :)
in that case you just go straight to the half angle substitution, and substitute (1/2-1/2cos(2t)) for sin^2t. then you just integrate term by term. make sure that when you take the integral of cos(2t), you use chain rule and divide by the derivative of the inside function, 2t. then evaluate at your limits of integration. :)
Holy cow! the blackboard and the chalk are as real as they get... thanks for the help, appreciate it.
I'm glad I could help!
Excellent explanation... please post more video on math. Best math teacher. Good work. Thank you.
I'm referring to integrating this specific type of function, that is, a product of sine and cosine. :)
Sine and cosine terms come up a lot in e.g. electrical engineering when AC currents are being dealt with. So it's not improbable that if you're working in such a field you'll meet one.
Simply perfect helped so so so so much.every video is phenomenal.
+Mehtab Ahmed Thank you so much!
You're my hero I can't thank you enough. If it was not for you, I would have failed
Mohammed Alkhaldi I'm so glad I could help!!
I calculate it using Pythagorean identity and reduction formula (derived by parts with pythagorean identity)
elegant explanation
Very helpful Thank you!
you're welcome!! :)
what if the problem was just y= integral from 0 to x times (sin^2t)dt ?
would i just plug in the substitution? i'm so confused!
Your videos are excellent! You explain very well! Keep it up! :)
Thanks Daniel!
hi! can you do a video on how IBP was formulated? thanks!
thanks! :)
thank you!! :)
Thank you for the help :)
you are a hero
+Shambhavi Kalra Thank you!
Did you get the (sinx)^2 = (1/2)(1-cos(2x)) from the sinxcosx = (1/2)sin2x on the left? or is it a seperate identity? Thanks v much x
Karl Roberts I wonder that too 😐
Rewrite trig function with sec(x) and tan(x) or cos(x) and sin(x)
From Euler substitution we will get
sec(x)=u-tan(x) for sec(x) and tan(x) version
or
cos(x)=(1-sin(x))u for cos(x) and sin(x) version
lol, no problem! :)
128√ey80...:)
Excellent!!!
+joliettraveler Thank you so much!
Perfect thanks!
What if m and n are different numbers ? We are left with (sinxcosx)^m(cosx)^n-m
It's a separate identity! :)
or you can use power reducing formulas.
lol... ya didn't catch that until afterwards. :) btw, thanks for responding to jeremy0203 in the first place!
i did this for sin^2(x)cos^4(x) and got stuck when i end up with (1-cos(4t))(cos^2(t)) I dont know how to remove the cos^2(t). I know I can use 1/2(1+cos2t) but that doesnt make it any simpler, since i end up with cos4t and cos2t multplying, can anyone explain?
You rock -333
What real world use do these prolems have than being able to do them on say an exam.
thank u-- happy new year
think of your mother/sister/wife/girlfriend etc. before you say that.
you're welcome!! :)