that's because you're focusing on how the teacher solves a problem and not focusing on the formula. When you familiarize the formula, all you have to do is substitute variables and simplify it with basic algebra. The biggest problem is if you take a calculus course without mastery in algebra.
@@damontayy1272 Calculus has so many formulas, memorizing them isn’t gonna help, you need to physically imbed the fundamental concepts into your mind to familiarize the other concepts
@@jorgegarza4172 I know. But guess what, you have to do hard shit to be able to amount to something. Your professor won't change the syllabus, you have to comply or shift to culinary school.
That is a common fallacy and the way it is taught. It is a failure as John Gabriel has shown clearly on his New Calculus channel. This is amazingly simple process and so much saving. This channel shouldd give up their name because he provides nothing but fast answers while New Calc channel does this with the process and the answers come simply. @@jorgegarza4172
That's a shortcut for u-sub that only works in special cases. So when you use that shortcut, you _are_ using u-sub. Just like how the method of evaluating rational limits at infinity is just a shortcut for L'Hopital's Rule that only works for certain types of rational/radical functions. But yes, you're right, you don't explicitly have to do the working for it, but this channel was made for beginners.
Exactly, That is a common fallacy and the way it is taught. It is a failure as John Gabriel has shown clearly on his New Calculus channel. This is amazingly simple process and so much saving. This channel shouldd give up their name because he provides nothing but fast answers while New Calc channel does this with the process and the answers come simply. No more unnecessary steps as part of a long and tedius process.
you don't even need to use substitution for such a simple problem like this, just know that for (x+a)^n, with a being a constant and n being a whole number(negative or positive integer, both work), by integrating you always get [(x+a)^n+1]/(n+1), it's just a simple derivative
Correct. [(ax + b)⁽ⁿ ⁺ ¹⁾]′ = a(n + 1)(ax + b)ⁿ How would you answer the next question: ● Find the primitive function F(x) (i.e. F(x)= ∫f(x)dx) of f(x) = (ax + b)ⁿ (‼️whithout using the standard list of primitive functions.‼️) where x is in the Domain D ⊆ ℝ of f and n ∈ ℤ.
That is just because of the use of a U-Sub implicitly, this shows out the steps for that formula. Don’t remember a formula blindly without understanding it’s derivation
If this channel existed when I was preparing for my calculus exams 20 years ago, I think I would have gotten much better grades!... But RUclips ITSELF wasn't launched until 2005, so RUclips didn't exist at all when I was in university. Thanks for making me feel old. 😜 No, but seriously, thanks for these videos! You must be helping the next generation.
Okay so this helped me A LOT. Coming back to school (2 yrs) after being sent across seas and been thrown into a calc 2 class… I remember some things but the really helped me out!!
Not a speedrun at all. Just notice the derivative of that is 1, then treat (x + 2) as if it was what you’re integrating, and (1/3)(x + 2)^3. Should take you 1 or 2 seconds to solve
Oh I just develop the square of the binomial and integrate every term, but your metod it's Very good, if it is something basic, it should be noted that I am just learning to derive/integrate, so I don't know a lot of
Using the second fundamental theorem of calculus is clearer , just find the derivative of (x+2) , which is 1 , then mould it properly. Then you get the answer
Just use reverse chain rule, and you find out that you divide by 1 (because of the coefficient of x), so you simply have to use the reverse power rule.
This is because you were taught one way as you teach only one way. As if it were the only way. Sadly it's the only way you know and you provide so little worth to your students while you mimmic parrot as a career. Hero to no one.
Yes, but what if the integrand were (x+2)^137 ?. Or, worse still, if it were (x+2)^(3/5) ? Good luck raising (x+2) to the 137th power, or to some fractional power.... 😃😃 With u-sub, the problem is done exactly the same way: use power rule, then back-sub.
we still can't solve the integral of some basic mathematical functions For example, although we can calculate the result of the integral e^sin(x) dx numerically, we cannot express it symbolically. Mathematics is not a science, it is a language. #math #mathematics #integral #sinus #cosinus
You didn't need the du/dx, you could directly go ahead and substitute the u for x+2 and still get the same answer at the end. You made it way more complicated than it qctually is dude.
People will hate on me for this but i do not care. I never liked U sub and never will. I understand the concept and instead just solve the integral using the tabular table instead.
In normal way, by expanding (x+2) ^2 and integrating we get : ((x^3) +(12x) +(6(x^2))) /3 But through substitution method : ((x^3) +8+12x+(6(x^2)) ) /3 An additional 8 is coming!!!!!! Iam so confused. Can anyone explain plz 😢!!
@@vaishalikarande3246 don't worry, you will learnt all these and more in 2-4 years. Remember the derivative and integrals by heart. It is essential in Univeruty regardless which stream you choose.
reverse chain rule is just the consequence of a u-sub that always works: if ∫ f(x) dx = F(x), then: ∫ f(ax+b) dx {u=ax+b, du= a*dx, dx=du/a} = ∫ f(u) (du/a) = (1/a) ∫ f(u) du = F(u)/a = F(ax+b)/a see
Развлечения
Nah, true chads make it the integral of x^2 + 4x + 4 to get x^3/3 + 2x^2 + 4x + C
fact
now do that for (x+2)^20
@@m.guypirate6900 same stuff u gotta calculate in the end anyway
@@saturapt3229 no it isn't lol
Just use Pascal’s triangle lmao but good luck finding the coefficients
Calculus is like a Minecraft tutorial it starts off nice, and then the problem immediately starts using 335.67 different letters
Exactly, I was like,
Ok,
Ok, yeah that makes sense
...
WHAT THE F***
that's because you're focusing on how the teacher solves a problem and not focusing on the formula. When you familiarize the formula, all you have to do is substitute variables and simplify it with basic algebra.
The biggest problem is if you take a calculus course without mastery in algebra.
@@damontayy1272 Calculus has so many formulas, memorizing them isn’t gonna help, you need to physically imbed the fundamental concepts into your mind to familiarize the other concepts
@@jorgegarza4172 I know. But guess what, you have to do hard shit to be able to amount to something. Your professor won't change the syllabus, you have to comply or shift to culinary school.
That is a common fallacy and the way it is taught. It is a failure as John Gabriel has shown clearly on his New Calculus channel.
This is amazingly simple process and so much saving. This channel shouldd give up their name because he provides nothing but fast answers while New Calc channel does this with the process and the answers come simply. @@jorgegarza4172
This is a simpler problem that doesn’t require substitution, but does a good job explaining the overall concept
It took me 5 seconds to do it
Took me just a flich@@SuperStudiousman
kid named reverse chain rule then divide by derivative:
derivative named kid:
@@XanderAnimations lmaoo
You don't even need u-sub. Its a linear function with coefficient of 1, so du will just equal dx.
i think the point was for it to be an easy application of U sub. to make it easier to understand for beginners
Yeah but u sub is easier in this case
That's a shortcut for u-sub that only works in special cases. So when you use that shortcut, you _are_ using u-sub. Just like how the method of evaluating rational limits at infinity is just a shortcut for L'Hopital's Rule that only works for certain types of rational/radical functions.
But yes, you're right, you don't explicitly have to do the working for it, but this channel was made for beginners.
Exactly, That is a common fallacy and the way it is taught. It is a failure as John Gabriel has shown clearly on his New Calculus channel.
This is amazingly simple process and so much saving.
This channel shouldd give up their name because he provides nothing but fast answers while New Calc channel does this with the process and the answers come simply.
No more unnecessary steps as part of a long and tedius process.
Yeah but when co efficient isn’t 1?
Me watching this:-😵💫😵💫
you don't even need to use substitution for such a simple problem like this, just know that for (x+a)^n, with a being a constant and n being a whole number(negative or positive integer, both work), by integrating you always get [(x+a)^n+1]/(n+1), it's just a simple derivative
i'm sorry but my inner calculus is screaming PLUS CEE
Correct.
[(ax + b)⁽ⁿ ⁺ ¹⁾]′ =
a(n + 1)(ax + b)ⁿ
How would you answer the next question:
● Find the primitive function F(x)
(i.e. F(x)= ∫f(x)dx) of f(x) = (ax + b)ⁿ
(‼️whithout using the standard list of primitive functions.‼️)
where x is in the Domain
D ⊆ ℝ of f and n ∈ ℤ.
That is just because of the use of a U-Sub implicitly, this shows out the steps for that formula. Don’t remember a formula blindly without understanding it’s derivation
I’m pretty sure that’s already what U substitution is, it’s just giving a formulaic way of solving it.
My maths teacher always used to tell me that if it's a linear function in x then integrate it as you would just f(x) then divide by coefficient of x
yup, because
if
∫ f(x) dx = F(x) + c
then
∫ f(ax+b) dx
{u=ax+b, du= a*dx, dx=du/a}
= ∫ f(u) (du/a)
= (1/a) ∫ f(u) du
= F(u)/a + c
= F(ax+b)/a + c
Some people need long solutions and some don’t. This helped with integration of (a-x)^-2. Thank you.
Everything on RUclips calculus makes sense BUT when I get in class I’m dumb 😊
If this channel existed when I was preparing for my calculus exams 20 years ago, I think I would have gotten much better grades!...
But RUclips ITSELF wasn't launched until 2005, so RUclips didn't exist at all when I was in university.
Thanks for making me feel old. 😜
No, but seriously, thanks for these videos!
You must be helping the next generation.
Thank you very much, I was stuck on a problem like this today :D very good short!
Are you in high school?
Thank u 😭I've been trying to figure out the step after getting the u 😭
Me too
"first we need to find you"
PLEASE DON'T FIND ME!! I HAVE A FAMILY!!!!
idk why i but i lowkey find u sub fun and interesting to learn
Please make more of these
Okay so this helped me A LOT. Coming back to school (2 yrs) after being sent across seas and been thrown into a calc 2 class… I remember some things but the really helped me out!!
Why is bro making this simple problem so complex? 😂
You're the best rapping in math explaining congrats
You are the good Physicist!
I did a question like this in the same way coz my dumbass forgot there is a simpler rule for linear equation with exponents
Don’t memorize, think
Thank you
Thanks!!!!
thanks bro
Not a speedrun at all. Just notice the derivative of that is 1, then treat (x + 2) as if it was what you’re integrating, and (1/3)(x + 2)^3. Should take you 1 or 2 seconds to solve
Wait till trigo functions get involved
In general, integral of
f(ax+b) = (1/a)*F(ax+b)
“I don't integrate the question, l differentiate the
options”
~Ме
Now integrate √(x²+2x)
2/3 * 1/2x+2 *(x^2+2x)^3/2
Simplier without sub because we always can add const in differential: dx = d(x + const)
Man just add one to the power and divide by the new added power man making it so hard
I never learned this in school this is my first time
i found it before the video even started
Ok ok i subscribed. U earned it!❤
Where does the two other dx in the du=dx come from?
Oh I just develop the square of the binomial and integrate every term, but your metod it's Very good, if it is something basic, it should be noted that I am just learning to derive/integrate, so I don't know a lot of
yeah I'm taking AP Calc AB next year and It is wraps.
Day 1: Manifesting Desire
Day 2:
It’s tough for me figuring out what “u” is
The multiplying of both sides by dx caused me physical pain... smh
Why?
Math is so difficult nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai nai 😢
Like in chain rule in differentiation when you multiply the derivative
Why not divide the derivative in integration in this problem
just expand the x+2 to get the integral of x²+4x+4
Using the second fundamental theorem of calculus is clearer , just find the derivative of (x+2) , which is 1 , then mould it properly. Then you get the answer
Just use the reverse chain, substitution is not needed for problems like these
Question:
Is the reverse chain implicitly the u-sub approach?
U-sub is the reverse chain lol
I did calculus and the moment this all made sense was when I realised theirs who du de dx bullshit was what was confusing me😂
Just expand the bracket and integrate lol
For this specific method, we can just simply use antiderivative.
Sometimes U-sub is helpful sometimes it's superfluous.
or just write it as the derivate of ((x+2)^2)/2 so thats about it , u sub is used for problems that are so easy to use just directly
Just use reverse chain rule, and you find out that you divide by 1 (because of the coefficient of x), so you simply have to use the reverse power rule.
That's what u-substitution is.
du=dx so u sub isn’t necessary so you get 1/3(x+2)^3 +C or just expand it like normal people.
n i c e
linear inside so (x+2)^3/3 works no?
Isn't this more useful when numerator is the derivative of the denominator?
Bro made something so easy complicated
Just find the anti-derivative then you’re done
(x-2)^3
----
3
Math was easy before meeting calculas😂
how did I get here... what the fuck is an integral?
wow.. though there's a short way out to tackle it
i like u
There is no need for u sub. Make the 2 a then take that number flip it as if it was a fraction and multiply it to the front. Add c ofc.
what is this pre calc
I actually thought if he did it fast U-SUB(cribe)
I sub
3)
2
(2x)dx = ∫ [ f(x)]
2
f ′(x)dx = 1
3 ∫ [ f(x)]
3
+ c
= 1
3
(x2 + 3)
3 + c
dx = d(x+2)=dt
Int (x+2)dx = (x+2)^2/2 + const
Can you please tell us this real world use
What I tell my students:. U-sub is the Swiss army knife of integration techniques! 😃
This is because you were taught one way as you teach only one way. As if it were the only way. Sadly it's the only way you know and you provide so little worth to your students while you mimmic parrot as a career. Hero to no one.
holy crab
No need for substitution.
I forego the u sub and just perform the operation
Yes, but what if the integrand were (x+2)^137 ?. Or, worse still, if it were (x+2)^(3/5) ?
Good luck raising (x+2) to the 137th power, or to some fractional power.... 😃😃
With u-sub, the problem is done exactly the same way: use power rule, then back-sub.
But you can just expand lol
Just reverse chain rule?
t²dt
= t³/3
= (x+2)³/3
Plenty of alternatives. If you really wanted to waste your time, this can be done by parts.
(x+2)³/3 is right but not easy to calculate when x number
we still can't solve the integral of some basic mathematical functions
For example, although we can calculate the result of the integral e^sin(x) dx numerically, we cannot express it symbolically. Mathematics is not a science, it is a language. #math #mathematics #integral #sinus #cosinus
You didn't need the du/dx, you could directly go ahead and substitute the u for x+2 and still get the same answer at the end. You made it way more complicated than it qctually is dude.
My fellow idiot. You need to substitute dx with du. That's why he did ask the calculation.
(ax+b)^n has a formula use it
What the fuck is that "C" in the last step??
Just (x+2)^3/3+C
People will hate on me for this but i do not care. I never liked U sub and never will. I understand the concept and instead just solve the integral using the tabular table instead.
U don’t need u sub just do it in ur head it’s easy
If derivative of inner function is 1, no need to do u sub
In normal way, by expanding (x+2) ^2 and integrating we get : ((x^3) +(12x) +(6(x^2))) /3
But through substitution method :
((x^3) +8+12x+(6(x^2)) ) /3
An additional 8 is coming!!!!!!
Iam so confused.
Can anyone explain plz 😢!!
It's genuinely easier to just do it as it is
True, but this is a good demonstration of using substitution to solve the integral.
just use the power rule bro
What is a derivative
Not possible this answer check differentiate the integrated answer
Why use a U substitution? its a simple derivative?
Can you pls explain where did U come from?
It's just a placeholder to make the calculation simpler.
@@420sakura1 Thank you! Ohh so it doesn’t have any value it’s just like a bracket? (Me don’t know anything me in 8th st.)
@@vaishalikarande3246 don't worry, you will learnt all these and more in 2-4 years. Remember the derivative and integrals by heart. It is essential in Univeruty regardless which stream you choose.
Thank you so much for your fast reply and tips 😊😊!!
why didn't you use ∫(ax+b)^n dx=[(ax+b)^n+1/(n+1).a] +c
S (x+2)²
= S x² + 2² + 4x
S [x²] + (S [2²] = 0) + S [4x]
S [X²+2x] = X³/3 + 4
What did I do wrong?
U was completely unnecessary lol, this is just the power rule of anti derivatives
As a beginner ,why can’t we use the (a+b)^2 identity and then integrate each function separately?
correct, im puzzled why they have chosen this way
You can. Integral may have different forms of answers but if you were asked to find a limit. They would all be the same
U can,the answer will be the same
But the susbtituing approach is simple
Just use reverse chain rule it’s faster
I can't believe that I finally found someone who said this. I hate it so much when people use u-sub for such simple integrals like this one.
its the same
reverse chain rule is just the consequence of a u-sub that always works:
if ∫ f(x) dx = F(x), then:
∫ f(ax+b) dx
{u=ax+b, du= a*dx, dx=du/a}
= ∫ f(u) (du/a)
= (1/a) ∫ f(u) du
= F(u)/a
= F(ax+b)/a
see
They are the same thing lol
U-sub? More like “U deserve more subs!” 👍
So bad
@@gamerfanletsplay9302 Then my work here is done. But if you ever want to hear a pun on a particular topic, just let me know and LetsPlay!
Da hail?
tf did any of this mean? My exam is in like less than an hour too 😂. I dont like maths 😂.
For me?