I like how calc isn't about learning calculus, it's about memorizing a bunch of identities that you should've learned years ago
@carultch
Жыл бұрын
One trick is to learn to re-derive the identities from examining key points. As an example, I recognize from playing with my graphing calculator that both sin(x)^2 and cos(x)^2 can be re-written as a single trig function of twice the frequency. All that's left to do, is adjust the amplitude, phase, and vertical offset, to match it to the function of interest To show how it works with sin(x)^2, we start by evaluating a few key points: sin(0)^2 = 0 sin(pi/4)^2 = (sqrt(2)/2)^2 = 1/2 sin(pi/2)^2 = 1 sin(3*pi/4)^2 = 1/2 sin(pi)^2 = 0 This tells me that the function needs a midline of 1/2, a local maximum at (pi, 1), and a local minimum at (0, 0). Cosine starts on a peak and "coasts" downward, so we negate it to make it start on a valley and climb upwards. We then add 1/2 to it, and give it an amplitude of 1/2, to get our identity: sin(x)^2 = -1/2*cos(2*x) + 1/2
@Klaus-Schwab_Dictator
Жыл бұрын
😂
@tzonic8655
3 жыл бұрын
Even though It's been more than 2 years that ive finished my 3 calc Classes,i enjoy so much all your videos, thank tou so much for all ths help steve!
@rogerkearns8094
3 жыл бұрын
Didn't know about that sinAcosB formula, thanks.
@Vikingman2024
Ай бұрын
Great help! Thank you!
@kassidydavis5565
2 ай бұрын
I absolutely love how you explain and the examples that you put! You’re making me feel like I will be able to integrate one day 😂🤣❤️❤️🤞🤞🤞
@S21-rp5pe
3 ай бұрын
Thank you for the great explanation 🙏🏻 but I wanna ask about what should I do if I have the integration of sin * cos and they both have odd powers ,please help🙏🏻🙏🏻🙏🏻
@viliuskese3487
3 ай бұрын
you are a legend laughing at these integrals mate, good luck to you
@mrmoonmini
3 ай бұрын
love the concept of sine integration ❤
@tuinderdome
3 ай бұрын
Thank you very much sir!
@dfsgjlgsdklgjnmsidrg
3 жыл бұрын
where do i learn all the identities
@LiamFranklinFarang
6 ай бұрын
Trig 😂
@buhle2419
3 жыл бұрын
Thanks! I learnt a lot !!...
@mimzim7141
6 ай бұрын
Or use the well known identity: sin^2*cos^5= cos^5+cos^7
@H3XED_OwO
5 ай бұрын
i hate trig but sometimes it's stupidity makes me cackle
@mimzim7141
5 ай бұрын
Sorry i ment sin^2*cos^5= cos^5-cos^7 of course.
@lanomusambazi8654
2 жыл бұрын
Thank you so much sir for the knowledge. I have learnt the technic of trig integrals. I'm kindly asking for trig integrals of CSC and COT. Secondly, how do we integrate when sec power is odd? I will appreciate your soonest response. Thank you.
@nasaalfarah5652
11 ай бұрын
When secant power is odd, u=cosx. You take out a cos^2(x) from however much cosine you have. Finally you replace cos^2(x) with 1-sin^(x) and integrate and simplify at the end.
@Salamanca-joro
5 ай бұрын
Thank you man you are legned
@Krageon-Offline
2 ай бұрын
where can i get that shirt
@dioutoroo
2 жыл бұрын
Thank you, Sir!
@mrchiddy3628
Жыл бұрын
I have an next offer of calc Monday thick i will do it better for this tips
@jesemepardens9151
2 жыл бұрын
8:18 Otherwise with the other formula ( cos(a)cos(b) = 1/2(cos(a-b)+cos(a+b)) ) this would give us : 1/2intg(cos(3x)+cos(-x)) = 1/2intg(cos(3x)-cos(x)) = 1/2(1/3sin(3x)-sin(x)) = 1/6sin(3x) - 1/2sin(x) +C (haha almost forgot that one)
@hugodhia5707
Жыл бұрын
Is it actually the same with that in the video?
@jesemepardens9151
Жыл бұрын
@@hugodhia5707 I don't think so. Why would I have commented otherwise? The solution is the same though
@hugodhia5707
Жыл бұрын
@@jesemepardens9151 I thought it is just a different way to get the same solution. So, does that mean an integral can have more than one solution?
@jesemepardens9151
Жыл бұрын
@@hugodhia5707 it is a different way. I don't know how but the result is the same ! The method I used is legit
@tarfaibrahim912
8 ай бұрын
Identity memorising or understanding is the key points ....u can't jump to learn calculas without learning more basic trig algebra !!! But u can practice the ideas
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