I definitely prefer the u-sub approach of form 2 (especially regarding the last example question with the sqrt() on the bottom. I think for form 1 the approach makes sense but it becomes too much of an algorithm for form 2 and to me at least that is not how it should be.
Great video and really useful, especially for form 1 but I just think its better to understand each question and to use the u-sub, cancelling out terms.
The minus sign comes from differentiating cosx. Differntial of cosx =-sinx and it's cos2x so you always multiply the number with x while differentiating, hence making -2sin2x . Hope that clears out ur confusion
You can use integration by substitution. Set u= 1 + tan^2(x). Get the integral in terms of u; then integrate. The final step is to replace the u with 1 + tan^2(x). Don’t forget to include the constant of integration C.
For an equation where y= a^x 1)Take ln of both sides then take e of both sides but without cancelling the x terms side so giving u Y= e^ln|a^x| 2) using the natural logs rules we can change this equation to the form Y= e^xln|a| Now u see x is no longer a power of a within the brackets of ln but multiplied by ln|a| 3) it is not in a form we can differentiate and so dy/dx = ln a (e^xln|a|) Now we do the opposite of what we did initially and make x a power of a and cancel out ln and r so we r left with Dy/dx = ln a (a^x) We did all this to basically change an equation into a form we know how to differentiate then differentiate then simplify it back so in short If y= a^x Then, dy/dx = ln a (a^x)
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You are probably the only one on the whole internet who has explained integration in a very intuitive and easy-to-understand way. Thank you!!!
This man is saving our lives.
SOOOOO helpful!! PLEASE do stats and mechanics year 2 I am finding it hard :(
Two more chapters of year 2 pure, then I’ll be moving onto year 2 statistics and mechanics 👍🏻
@@zeeshanzamurred9280 Thank you SOO MUCH!! you're too kind
I will never forgive the man that disliked this video
13 idiots have disliked this masterpiece
@@WowTooCool being 3yrs bro
Dude you're actually a life saver😂 can you become my maths teacher?
Just found your videos and they are sooooooooo helpful, like i'm in a real classroom. Thank you so much for teaching us!!!!😭😭
Absolutely insane stuff, thanks I now love integration
Your videos are extremely helpful!! Thank you !!
Professionally executed and most helpful
Best teacher ever! Love the clear explanation, thank u!
Me: [failing math]
Zeeshan: “come this is no place to die”
Can you show us how to solve differential equations by integrating factor?
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I definitely prefer the u-sub approach of form 2 (especially regarding the last example question with the sqrt() on the bottom. I think for form 1 the approach makes sense but it becomes too much of an algorithm for form 2 and to me at least that is not how it should be.
Great video and really useful, especially for form 1 but I just think its better to understand each question and to use the u-sub, cancelling out terms.
Thanks brother ❤️❤️❤️....your videos are life saver ❤️❤️❤️
THANK YOUUUUUUUUUUUUUUUU
THANKYOU
omds you’re too sick thankyou !!
Great video bud!! 😍😍
Couldn’t the 6th question be form 1 if you apply tanx identity and make the integral negative?
Great Expectation 👌👌👏👏👏👏
Very clear explanation. Thank you sir.
My man definitely nailed it, thanks
best teacher even better than my school teacher
The best of every video I've seen on net
seriously thank u
this might be silly question, but where does the -2 come from in -2sin2x when you do dy/dx for the first question at 8:35? why would it not be 2cos2x?
The minus sign comes from differentiating cosx. Differntial of cosx =-sinx and it's cos2x so you always multiply the number with x while differentiating, hence making -2sin2x . Hope that clears out ur confusion
@@googleit2321 thank you very much! Since posting my comment, I've become more confident in my integration skills ((:
Thanks
bro came in clutch
how did u get -2sin2x from dy/dx of sin2x? 17:50
I think you mean at around 08:30, check what he set y equal to ---> y = ln (3 + 2cosx) then he finds dy/dx of that.
this was really helpful thank you.
Thanks brother. You saved my time🙂
For no3 2hy did you say cot2x^2
Because originally it's cot2x^1, so f(x)^n+1 is cot2x^2
hw do u integrate this question : integration of sec^2 x (1+tan^2 x)
You can use integration by substitution. Set u= 1 + tan^2(x). Get the integral in terms of u; then integrate. The final step is to replace the u with 1 + tan^2(x). Don’t forget to include the constant of integration C.
Can u also use reverse chain rule ?
Yes you can. You’ll have to expand the bracket and then use the reverse chain rule on the second term.
thank you for this video it really helped me
love you brother
thank you so so much!
MY GUYYY!!!!!!!!
Sir what's the general rule for integrating A^x ?
E.g integral of 2^4x
For an equation where y= a^x
1)Take ln of both sides then take e of both sides but without cancelling the x terms side so giving u
Y= e^ln|a^x|
2) using the natural logs rules we can change this equation to the form
Y= e^xln|a| Now u see x is no longer a power of a within the brackets of ln but multiplied by ln|a|
3) it is not in a form we can differentiate and so dy/dx = ln a (e^xln|a|)
Now we do the opposite of what we did initially and make x a power of a and cancel out ln and r so we r left with
Dy/dx = ln a (a^x)
We did all this to basically change an equation into a form we know how to differentiate then differentiate then simplify it back so in short
If y= a^x
Then, dy/dx = ln a (a^x)
Is there a quick way to differentiate the ln functions in this video as I have to do it letting u=x e.g
sir for the last question(example 4 ), why cant form 1 work?
Very very juicy method zeehsan
thank you so much from an IB student
shouldnt it be -2cos2x at 8:35 ? (differential of sin2x)
he's differentiating the 3+cos2x
@@emaanqu123 right tyy
i love you Zeeshan Zamurred
hi sir , what happened to the 2x+1 in question 4?
Thank you king
love ya sir
What a man
than k yuou very helpful!
🕋
god bless you
afdshjfhj i can't believe i survived P3 and P4 integration for so long without knowing this. tysm this was extremely clear.
thank you, thank you, thank you, thank you, thank you, thank you *100000000000000
Do think you will finish the content before our exams
Hopefully I should be done by then 👍🏻
coronavirus: im about to end your career
you should've done question 4 from the textbook
Legend
drawing the rectangle step is a game changer 👁👄👁
how to integrate xe^x^2
You can use integration by substitution. Your substitution would be u=x^2.
exam is in 3 hours and im learning this
That intro makes me laugh every time
please reply to me sir i'm your biggest fan
Proof that not all heros wear capes
The absolute fucking goat
who is here ready for the first autumn a levels maths retake
you should be my father
Thanks