Absolutely! Differentiation is the key to integration - I recommend asking yourself “what differentiates to this function” instead of “integrate this function”. Originally integration was called anti differentiation!
It has ‘gone’ because when you differentiate what we wrote as the answer, you get the extra cosx coming back again because of the chain rule! The fact it was there in the thing we were integrating to begin with was helpful, because it came from the result of differentiation using the chain rule! Hope that helps!
@@BicenMaths thank you i now understand from this and watching a latter video that the reverse chain rule is only applied when the outer function looks like it could have been created from differientiaitng the inner function Thank you your the best maths teacher ever I hope you get knighted someday
Because when you integrate e^x it integrates to e^x - in other words, the power remains the same. You only increase the power by one for polynomial terms, and this is an exponential!
Mr Bicen, as I am self-studying I don’t have access to the topic tests that are generally done in schools. Do you have any suggestions on how I can perhaps devise a topic test for myself to test my understanding of the A2 content I have covered so far?
I would offer you these options: 1) access my exam questions file in the Bicen Maths Google Drive here, and select some from the already categorised topics that have a reasonable number of marks. Try them in exam conditions drive.google.com/drive/folders/1uUbx_lRLLE9O4WnI8TS77dUOJw_DjljV 2) use the mixed exercises from the textbook and randomly select a set number of questions to do in timed conditions 3) perhaps better than the mixed exercises, use the review exercises from the textbook, as they are past exam questions and tell you how many marks they are worth - then you can calculate the amount of time you’d have by multiplying the marks by 1.2 to get the number of minutes you’d have in the exam! Hope that helps!
hi sir, on the very first slide in this powerpoint on the first question how come in our answer there was no x at the front like there was in the integral given?
If there was an x, when you would differentiate it, you'd need the product rule, so it wouldn't return to the integral in the question. The extra x appears from the chain rule when differentiating the expression we get as the answer!
@@BicenMaths so the integral sign is almost like saying dy/dx = whatever is in the integral then finding the y equation that differentiates back to the integral
@@ehehrrhr That's exactly it! I tell my students how integration used to be called anti-differentiation. And that's how you should think of it, it'll really help with your understanding!
Hi sir really quick question how would you know when to use reverse chain rule or when you can just standard formula method in order to integrate thanks
Spend time getting really good at differentiation - the chain rule, particularly! Try and know what all functions differentiate to - that'll help you think about what has been differentiated to give you the thing we want to integrate
Because we’re trying to integrate something to the power of 3, and this usually goes to something to the power of 4, right? So it’s the same idea for the reverse chain rule here. Hope that helps.
Because we know that (sinx)^3 would go to 3(sinx)^2 cosx using the chain rule, which looks pretty similar to what we are trying to integrate! You have to really be good at the chain rule to spot these things!
what a legend you are mr bicen, will forever be known as the maths lifesaver
Thank you 🙏🏼 🤩
Three years later, I'm watching this on the same date lol.
watching this the morning of my a level exam haha
Idiot
how did it go🤧
^
so basically to be good at the reverse chain rule you have to be VERY good at differentiation lol
Absolutely! Differentiation is the key to integration - I recommend asking yourself “what differentiates to this function” instead of “integrate this function”. Originally integration was called anti differentiation!
what happened to the cosx when we intergarted the cosx^2sin
It has ‘gone’ because when you differentiate what we wrote as the answer, you get the extra cosx coming back again because of the chain rule! The fact it was there in the thing we were integrating to begin with was helpful, because it came from the result of differentiation using the chain rule! Hope that helps!
@@BicenMaths thank you i now understand from this and watching a latter video that the reverse chain rule is only applied when the outer function looks like it could have been created from differientiaitng the inner function
Thank you your the best maths teacher ever
I hope you get knighted someday
why did we not raise the power of the 'consider e^x2+1' by one? 16:48mins thank you!
Because when you integrate e^x it integrates to e^x - in other words, the power remains the same. You only increase the power by one for polynomial terms, and this is an exponential!
Mr Bicen, as I am self-studying I don’t have access to the topic tests that are generally done in schools.
Do you have any suggestions on how I can perhaps devise a topic test for myself to test my understanding of the A2 content I have covered so far?
I would offer you these options:
1) access my exam questions file in the Bicen Maths Google Drive here, and select some from the already categorised topics that have a reasonable number of marks. Try them in exam conditions drive.google.com/drive/folders/1uUbx_lRLLE9O4WnI8TS77dUOJw_DjljV
2) use the mixed exercises from the textbook and randomly select a set number of questions to do in timed conditions
3) perhaps better than the mixed exercises, use the review exercises from the textbook, as they are past exam questions and tell you how many marks they are worth - then you can calculate the amount of time you’d have by multiplying the marks by 1.2 to get the number of minutes you’d have in the exam!
Hope that helps!
Thank you, this is very helpful 😊.
If you still need them i can email you some materials from my school you can use as topic tests
Hello sir, at 14:07 what would you consider then if denominator was the derivative of numerator?
Wouldn't work with reverse chain rule - only works if numerator is derivative of denominator!
hi sir, on the very first slide in this powerpoint on the first question how come in our answer there was no x at the front like there was in the integral given?
If there was an x, when you would differentiate it, you'd need the product rule, so it wouldn't return to the integral in the question. The extra x appears from the chain rule when differentiating the expression we get as the answer!
@@BicenMaths so the integral sign is almost like saying dy/dx = whatever is in the integral then finding the y equation that differentiates back to the integral
@@ehehrrhr That's exactly it! I tell my students how integration used to be called anti-differentiation. And that's how you should think of it, it'll really help with your understanding!
Seb I was doing this and 11.3 recently in class (we use the same slides that u used) and I'm really finding it tough
nvm I'm getting reverse chain rule now, 11.3 and 9.6 still tough
They're hard! Let me know if you have any questions, happy to help!
Hi sir really quick question how would you know when to use reverse chain rule or when you can just standard formula method in order to integrate thanks
Actually not that simple a question! But I answer it in detail here ua-cam.com/video/L6UkjiDVmWk/v-deo.html
At 10:05 you can call it the derivatand ?
I’ve not heard this used before, so I wouldn’t use it personally!
@@BicenMaths i know. With your dedication to maths, you have earned the privilege to coin a word for that 👍
What is the best way to learn how to 'consider'
Spend time getting really good at differentiation - the chain rule, particularly! Try and know what all functions differentiate to - that'll help you think about what has been differentiated to give you the thing we want to integrate
sir, why did the bracket rise to the power of 4 at 3:13
Because we’re trying to integrate something to the power of 3, and this usually goes to something to the power of 4, right? So it’s the same idea for the reverse chain rule here. Hope that helps.
@@BicenMaths thankss sir, I've learned a lot from your helpful videos
Hi sir at 7:19 why do we consider it to be sin^3 x
Because we know that (sinx)^3 would go to 3(sinx)^2 cosx using the chain rule, which looks pretty similar to what we are trying to integrate! You have to really be good at the chain rule to spot these things!
great video seb
very helpful , thanks
Life saver...
U ARE SAVING MA LIFE
bicen too good