What is the Meaning and Usage of the Integral Sign?

[nirky]

what does this --> ∫ mean and what how do you use it? Thanks.

 

[ShayanJ]

Its an integral sign. If used with boundaries($\int_a^b f(x) dx$), it denotes the area of the region bounded by x=a and x=b and y=0 and y=f(x). If used without boundaries($\int f(x) dx$), it denotes a function $F(x)$ such that $\frac{d}{dx}F(x)=f(x)$.

 

[Akorys]

I would like to expand a bit in case you wanted to know about how you would find the solution to $\int f(x)dx$ for some function f. It does not have a formula, as a derivative would have in the form of a limit of a secant, which makes evaluating integrals generally more complicated. There are ways to come up with "nice" formulas for certain functions, but some cannot be expressed easily. If you wanted to use the integral for some given function, you may search for integration laws on the internet, and you are bound to find what you need as long as your function is not too complicated.

 

[Ssnow]

In simple terms you can see the operator $\int \ \ \cdot \ \ dx$ as the inverse of the derivative. It represent a family of functions, you can observe that the derivative of $x^{2}$ is the same as the derivative of $x^{2}+c$ with $c$ a constant.