can i divide the integral by 2 like this
#integral
gleaming vapor
prime birchBOT
can i divide the integral by 2 like this
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delicate python
can i divide the integral by 2 like this
Not like that, no.
What you can do is u substitution.
radiant portal
No try to imagine it like a function , you have a function and have area between two limits diveded by 2 but you half both the limits . Will that be true ?
delicate python
then how can i solve this
Like I said, u substitution.
gleaming vapor
Like I said, u substitution.
i tried it as you can see from the first pic . do you mean substitute a’s with u too. if so i don’t know how to.
wait
ok
a is actually x
delicate python
i tried it as you can see from the first pic . do you mean substitute a’s with u...
Okay, you know how when you do a u substitution, you re-substitute x back in at the end?
delicate python
a is actually x
No.
gleaming vapor
Okay, you know how when you do a u substitution, you re-substitute x back in at ...
i dont know how to do a u substitution here
delicate python
i dont know how to do a u substitution here
Just, look. You know that part, right?
gleaming vapor
what part
delicate python
The part I just explained.
The part you just replied to.
But didn't actually respond to.
gleaming vapor
you mean like in the end you have a function like for example f (u) du and since everything is in u form you write it like f(x) dx?
delicate python
...no.
I mean.
You have a function of x.
You do a u substitution.
You integrate.
And then you reverse your substitution.
Because your initial integrand was a function of x.
Therefore your final answer must be a function of x.
Do you know how to do u substitution at all?
gleaming vapor
yes
delicate python
Okay. Integrate (2x + 3)^2 using u substitution.
delicate python
Why is your result a function of u? You integrated a function of x.
A function of x.
I mistyped.
gleaming vapor
okay i can write it like 1/2.x3/3 +c
delicate python
...okay, so differentiate that.
gleaming vapor
...okay, so differentiate that.
x2/2
delicate python
Yes.
gleaming vapor
where did i do it wrong
delicate python
You can't just replace u with the letter x.
You have to replace u with the equivalent value in terms of x.
gleaming vapor
so 2x+3
delicate python
Yes.
gleaming vapor
yes yes i get it
delicate python
So here's the thing.
When you're doing a definite integral, you could do that.
Or, equivalently, you could recalculate the bounds of integration to be in terms of u instead of x.
gleaming vapor
yes i know that actually
delicate python
...given that you didn't even know to plug back in the value of u after u substitution, I doubt it.
But let's look at our first integral here. u = x + 1. So then our bounds of integration in terms of u are...?
gleaming vapor
i actually knew it really… but used to always do it in definite integral and since there is only u , i converted it to x without thinking about it
delicate python
...if you knew it, I don't know how you're having trouble on this problem, because it literally is just recalculating the bounds of integration in terms of u.
gleaming vapor
But let's look at our first integral here. `u = x + 1`. So then our bounds of in...
i dont know because the bounds does not even have x it has a
delicate python
...so then you don't know how to recalculate the bounds of integration.
gleaming vapor
ok i dont know z i actually know but i guess you wont tell me how to do it unless i say “i dont know”
delicate python
i dont know because the bounds does not even have x it has a
This is not something that anyone who actually knows what I'm talking about would ever say. This is not a confusion you would have if you knew how to do this.
gleaming vapor
This is not something that anyone who actually knows what I'm talking about woul...
okay
delicate python
Look.
We're integrating from x = a - 1 to x = a + 3. If u = x + 1, then when x = a - 1, u equals what?
gleaming vapor
a
delicate python
Right. And when x = a + 3, u equals what?
gleaming vapor
a+4
delicate python
Right.
delicate python
It's okay to not know things. We're here to teach you. You just need to admit to what you don't know so that we can teach you it.
gleaming vapor
yes of course, but i just felt so humiliated because of the brain in your profile pic and the assertiveness in the way you write
but its okay thanks
gleaming vapor
It's okay to not know things. We're here to teach you. You just need to *admit* ...
thank you so much i solved it and would never forget how to substitute thanks to you :)))