What is an integral and how do I learn this?

I think it's Lowtax's ex-girlfriend

File: areaundercurve.png (13KB, 1273x713px) Image search: [Google]

13KB, 1273x713px

>>8399324
The value of the area under a curve is the integral of that curve. You can calculate that area for a range, or for all values of x and get a new curve as a result.

>>8399324
>What is an integral
>>8399353 this
> how do I learn this
by looking up any maths textbook or googling it, It's not that fucking hard.

[eqn]\int_{a}^{b} f(x) \; dx = \lim_{n \to \infty} \sum_{k=0}^{n} f(x_k) \Delta{x}[/eqn] Where [math]\displaystyle \Delta{x} = \frac{b - a}{n}[/math].

>>8399324
It's an inverse operation to derivation. Don't listen to others.

>>8400195
>It's an inverse operation to derivation. Don't listen to others.

That is the definition of an anti derivative.

Historically, the integral has referred only to the area under a curve. Initially we could barely tame curves so it stayed that way, as a weird idea floating in the air.

Then it started referring to the methods we used. So the Riemann Integral, for example, was born.

But integral has never referred to the anti derivative, it is just that mathematicians have found a relationship between the integral and the anti derivative of a curve.

>>8399324

It's literally just finding the area of a parallelogram repeatedly.

>>8400242
Not OP but when I set up a rotten integral and let it tend to infinite I get the (sum=integral) but how does that work??? Like the integral is a reverse derivative I just get so baffled by that idea

File: Planet of the sluts.gif (4MB, 700x298px) Image search: [Google]

4MB, 700x298px

>>8399842
>Riemman integrals

A continuous sum

>>8399324

Basically a way to find the area under a curve within a certain given interval. You basically take the anti-derivative of the function of which you want to find the area and replace the x values with the values of the interval. Then you subtract the the anti-derivative of the upper value of the interval with the anti-derivative of the lower value of the interval.

Once you master basic integral calculus, you can try to find volumes of three dimensional objects using surface-integrals and solid of revolutions

>>8399324
It can be viewed as a way to sum an uncountable amount of values.

>>8401208
Very nice way to look at it.