Mathematical analysis

Derivation formulas, integrals, primitive formulas volume rotational bodies

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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