Integration can be used to find areas, volumes, central points and many useful things. But it is often used to find the area under the graph of a function.
The process of finding a function, given its derivative, is called anti-differentiation (or integration). If F'(x) = f(x), we say F(x) is an anti-derivative of f(x).
Integration is the reverse of differentiation
A Indefinite Integral has no start and end values. In other word, there is no limit.
ddxF(x) = f(x) ⟺ ∫f(x)dx = F(x) + C
This is called indefinite integration,
A Definite Integral has start and end values.
The definite integral given by a function f of a real variable x and an interval [a, b] of the real line.
∫ f(x) dx = [F(x)]ba = F(b)-F(a)
And replace b by a, we should have the answer to be 0 because the area under the curve from b = a to b = a, should obviously be 0.
Some of the important integration formulas are listed below :-
1.For an example ,find the integration of
Some other important formulas given by.
Some inverse formulas.