What is it?
Integration is to Integrals the same Differentiation is to Derivatives. Both involve shrink a number down to its infinitesimal scale to calculate something. In the case of Integration, they are the about adding up infinitesimal pieces of something and calculating the area under a curve.
The objective of integration is to discover the integral of a function, also commonly named as antiderivative and primitive function. In other words, if you have a derivative , the original function is our antiderivative, the function integration wants to discover.
Integration Rules
Calculus’ first fundamental theorem states that the integral of a derivative of a function, is the function itself, except for a constant value. Because of it, the rules used in Differentiation can be applied to integration, just in reverse.
For example, the Power Rule in Differentiation can also be applied to integration, but instead of subtracting, you add the exponent.
f'(x^2) =2x\quad \text{and} \quad\int(2x)dx = 2x$$ > You can check the rules used in *Integration* by [[Differentiation rules.png|clicking here]]. ___ >*I got so fed up of calculus this semester, that i'm declaring this W.I.P.* *Consult [[Calculus ALL IN ONE - Mark Ryan.pdf]] or [[Calculus Early Transcendentals, 6th Edition (James Stewart).pdf]] for now.*