Integration is nothing but some.
It's just by creative imagination that.
If you stretch the s symbol of submission.
It becomes the integration symbol.
That's how you get remember, what is integration?
It's nothing but some action.
So now you will have a question that for summation, we already have a Greek symbol, Sigma.
Then why a new symbol?
Sigma summation is four discrete inputs.
That is, if I want to sum up the number of students in each class in a school, I will use Sigma.
But if I want to find that from point A to point B, there are how many bacterias?
Then I will use immigration, so to sum up.
Continuous values like this.
I use.
And we should use.
Integration.
Integration is just the inverse of differentiation.
Let's say I have a function Y is equal to fix, then if I differentiate it, it's called F Dash X or
Y by the X, and if I try to integrate F X, then I get the original function effects.
For example, let's say you want to integrate the below equation.
As power rule, integration of X-rays to N be X is equal to x rays to N plus one divide by N plus one
plus see that N is not equal to minus one.
Now, see, over here is a constant why I'm putting C. over here, I'll explain you in the next slide.
No superpower rule if I integrate this equation excuse me, minus six X squared, plus X plus one,
because I get the answer is x rays to four by four minus two cube plus X squared by two plus X plus
C.
You can validate the same by applying this power rule.
Integration and differentiation are opposite to each other, for example, derivative of X squared is
equal to two X and integration of two X is equal to X squared plus C, we keep C or constant here because
we are not sure if there has been a constant while differentiation, because differentiating a constant
is zero.
So if I differentiate X squared plus three, the answer for that is also two X.
So let's see some of the list of integral families integral of one being is equal to explicit integration
of Ebix is equal to X plus C integral of x rays.
To end the X is equal to x rays to end plus one divided by N plus one plus C, which we just saw in
the power rule.
So more families integral of Senex vehicles is equal to minus codecs, plus C integral of POSIX, the
X is equal to sign explosive.
Integral of it is to be X is equal to areas to X plus C.
And last but not the least integral of one by XDA X is equal to natural log X plus C, integral of areas
to X is equal to areas to divide by a natural log of a plus.
See if it is greater than zero and is not equal to one.
So we covered all the regular and basic differential and integration rules.
Which we need to study quantum mechanics.
If any specific rule needs to be studied pertaining to differentiation and integration for quantum computation,
we will cover in that particular lecture.
For now, we are good to go.
Jess.