Integration : (ax+b)ⁿ type functions : ExamSolutions

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this channel is worth gold, cheers - easy explanations, systematic and on point all the time. Thanks

alvinlepik

He's showing how if you just integrated as you'd expect it to be initially, then if you took the differential again (via the chain rule) that actually the term you integrated is not equal to the differential of your result, so you need to know, when integrating, what fraction will cancel out that result such that if your integral were to be differentiated again, you would have an equation equal to the original term you started with.

RShahProductions

Thanks! I always knew this was basic, no one explained it to me well at school.

fallenhuman

so basically it's (ax+b)^n+1/n+1(a) + c

angielxf

finally get it, move the main co-efficient out of the integral, Raise the power, and multiply the new number by the inside derived. then reciprocate that number and multiply it by the co-efficient. then next multiply the term with the raised power and add c

ebadrahman

*Or you could think of it as dividing the bracket by the new power multiplied by the derivative of the bracket*
for e.g
Integration of (5x+2)^3

1. Add 1 to the power and divide by it
[ (5x+2)^4 ] / 4

2. Take the derivative of the bracket or in other words differentiate the bracket, and then divide by the result
Derivative of (5x+2) = 5 + 0
[ (5x+2)^4 ] / (4 * 5)

3. If youre integrating dy/dx or d^2y/dx^2 dont forget adding " + c " as in differentiating constants become 0

bilaltaj

You must get asked the same question often, but I would really like to know what system/software/hardware to record your working? When you are writing and moving your pen around and pointing at things it looks completely natural. Brilliant tutorial as always. Thanks 🙏

peterhunt

thank youu sirrr. u are a live saver. live long and prosper!!!!

ibrahimwaseem

MR SIDDERS - could you please explain to me though why you don't integrate that constant, e.g. the 7 or the 4 and why you are allowed to bring them out? I would've thought they'd become 7x and 4x but obviously not lol
Thanks again!

RShahProductions

thanks bro from 11 years ago.I can finally be confident in my Test which is in an hour lol

crazeagar

No. It is 4 multiplied by the square root of .... ., not the 4th root of .... which would be to the power 1/4 anyway rather than -4.

ExamSolutions_Maths

Thank you. You made this so much easier

RehannahB

Or..if you have a linear expression inside the brackets, that is when the highest power of the variable is to the power 1. For example:(3x+2)^4, just add 1 to the power which will be 5 and multiply the new power by the coefficient and divide the whole expression with that. In simple algebraic terms: if y=(ax+b)^n then the integral would be: (ax+b)^n+1/an+1

SabrinaXe

The way I learned integration is you make the power (n+1) and then divide with (n+1) but you are making the power (n+1) and dividing with a(n+1).I dont understand how and why a comes in the game :( your previous integral tutorial is also with power n+1 divided with (n+1), there is no a :(

hababambiz

im 28 years old, i took calc 1 twice (highschool cred didn't transfer), calc 2-3, differential equations and linear algebra, and Im sad to say that today I googled what an integral actually is

seanm

Ok I got it ... chain rule, instead of multiypling we divide but I was actually not derivating, integrating again the t and then multiplying, I really need to cover a lot of basics :(

hababambiz

At 8:20, why have you cancelled out??? When I differentiated it, I did 4(1.5)(7) giving me 42. dy/dx= 42(7x-3)^1.5.
As my final answer for the integration, I got =2/21 (7x-3)^1.5.
Please clarify. thanks

mh

You could for this type, but that defeats the point I want to make. You will eventually need to appreciate the inverse of the chain rule for further integration methods rather than learn formulas all the time.

ExamSolutions_Maths

where did 1/15 come from in the example at 04.10 ?

rubanimohammad

In the beginning of the video, around 1:59 - for the second example to integrate, why does the 7 come outside the integral symbol?

isaiahdadlani

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