Integration and differentiation

Integration and differentiation are two fundamental operation in calculus. Calculus is the branch of maths focused on limits, function, derivatives, integrals and series.

 

Differentiation

The Newton’s different quotient is:

The derivative is the value of different quotient when it approaches to 0.

The process of finding derivatives is called differentiation.

 

Antiderivative

Antiderivative or primitive integral of a function is a function F whose the derivative is equal to f

*c is there because the derivatives of a constant value is always equal to 0

The process of finding antiderivatives is called antidifferentiation

There are many techniques to do antidifferentiation, the most common are:

· Integration by substitution;

· Integration by parts;

· Integration by partial fractions.

 

There is a relation between differentiation and integration?

Yes, the relation between differentiation and integration is given by Leibniz Newton theorem. This theorem shows that an indefinite integration can be reversed by a differentiation and allows to calculate the definite integral of a function.