Indefinite integral

Let f a function, it is said that F is a primitive of f if F’ = f.

 

NOTE: if F is a primitive of f → F + k (k Є R) is a primitive of f.

 

The indefinite integral of f is the set of primitives of f:

Example: 1) ∫cosx dx = sinx + k; k Є R

  2) ∫3sinxdx =3 ∫sinxdx = -3cosx + k    k Є R

  3) ∫(e^x+3)dx = e^x + 3x + k      k Є R

 

 

Exercise. Solve:

a) ∫3x² dx =

b) ∫2sinx·cosx dx =

 

 

 

 

Solutions: a) x³ + k; b) sin²x + k