# Mathematical analysis

## Derivation formulas - table of derivatives elementary functions

 Rules of derivation

## Common integrals formulas

Rules of integrals

Integrals through parts

If are differentiable with continuous derivatives, then the functions fg, f'g and fg' admit primitives and  their sets of primitives are linked by formula

Changing variables

Let be I,J  two intervals of R and let and f two functions having the properties

1. are derivable on I;

2. g admits primitives (let be G a primitive of it).
Then the function admits primitives on I and the function is a primitive of , i.e.

### Applications of integrals in geometry

#### The calculation of flat area

If G is continuous functions subchart.
f:
[a,b]->R+, then the surface G is

##### The length of a function chart
 The length of the function chart f:[a,b]->R derivable having continues derivable, is
##### Aria side of a rotating body
 If is a continuous function, then the rotating body determined by  f has the surface done by
##### The volume of a body of revolution
 If is a continuous function, then the body rotation determined by f has the volume and

Keywords: derivation formulas, integral primitive rotational bodies volume formulas, mathematical analysis

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