I have since changed it in the original PDF - if you did answer it with x sin2x, then the correct answer is: (-1/2)xcos(2x) + (1/4)sin2x + c. I'll also pin your comment!
Fantastic overview of advanced integration techniques! Loved the examples and clear explanations of various methods. Really helpful for tackling complex problems. Thanks for the great content!
Nevermind, the function doesn't work unless you re-arange this way, even though you remove solutions. The model holds for when P is between 0 and 100,000 as that is the unit of P. As a follow up question, for re-aranging expressions like this, are we always expected to leave out the modulus?
@@be-mr3tj As soon as we move to ln to exponential we can remove the modulus. If you did want to sub in a value into the ln part and it becomes negative, you can just take the modulus of it and use the positive part, that's the whole reason we have the modulus sign when integrating to ln|x|
I am hoping to do this for Core Pure, but I'm not sure on timings just yet - in 2025 I enter a different phase of the year for me where I start preparing for live classes, etc., so I have a little less time than usual. I'm going to tackle the Applied stuff for normal maths first :)
0:00 Examples 25:42 Special cases 33:30 Substitution 42:00 Parametric integration 48:10 Differential equations 57:33 Trapezium rule 1:00:55 As a limit of a
For the 3rd question in the video, you wrote out xsinx as the integrand, when on the document it’s xsin2x, doesn’t matter too much though I guess
I have since changed it in the original PDF - if you did answer it with x sin2x, then the correct answer is: (-1/2)xcos(2x) + (1/4)sin2x + c. I'll also pin your comment!
Fantastic overview of advanced integration techniques! Loved the examples and clear explanations of various methods. Really helpful for tackling complex problems. Thanks for the great content!
What a lovely comment - thank you :) This wasn't an easy set of questions to plan, so I'm really happy you think it was a good overview :)
Well done on making it under 1 hour and a bit :)
I was so close to under 1 hour 😭
@@BicenMaths I know
Good luck on the core pure next
Methods of calculus in under 2hrs lol
For the differential equation question, how can you say modulus of p/(1-p)= just p/(1-p), when for a positive population, it would always be negetive?
Nevermind, the function doesn't work unless you re-arange this way, even though you remove solutions. The model holds for when P is between 0 and 100,000 as that is the unit of P. As a follow up question, for re-aranging expressions like this, are we always expected to leave out the modulus?
@@be-mr3tj As soon as we move to ln to exponential we can remove the modulus. If you did want to sub in a value into the ln part and it becomes negative, you can just take the modulus of it and use the positive part, that's the whole reason we have the modulus sign when integrating to ln|x|
Hi sir, how are you doing? Will you be making further maths chapter summaries any time soon?
I am hoping to do this for Core Pure, but I'm not sure on timings just yet - in 2025 I enter a different phase of the year for me where I start preparing for live classes, etc., so I have a little less time than usual. I'm going to tackle the Applied stuff for normal maths first :)
Will there be a recap on year 2 applied topics ?
Yes!
Is this on your Google drive?
Yes, linked in the description!
Sir please do M1 it would be big help if u start teaching m1😭🙏🏾
Although the videos aren't organised for M1, I do have loads of mechanics videos on my channel!
you wrote out question 3 wrong
answer should be (-1/2x)cos2x + (1/4)sin2x +c
Yes, correct! I have since changed the original PDF. It's so easy to copy things down wrong!
Hi sir. I sent you an email. Did you receive it?😊
I am not sure... but I have just replied to my emails today, so hopefully you have received one! If not, I'll check the spam folder...
Time stamps would make it better but otherwise good!
0:00 Examples
25:42 Special cases
33:30 Substitution
42:00 Parametric integration
48:10 Differential equations
57:33 Trapezium rule
1:00:55 As a limit of a
They were in the description already 😊