# 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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