2nd year of post-compulsory secondary education (Natural sciences).




The indefinite integral

The problem of finding areas

The definite integral

Finding definite integrals

Geometric applications


Thanks to the work of Barrow, Newton and Leibniz (the creators of infinitesimal calculus), two paths which had developed separately throughout the history of mathematics, for over more than 20 centuries, were combined in what is now known as integral calculus. 

One of the paths, the search for formulae to find the area of plane regions, dates back to the ancient Greek mathematicians.

The other path emerged to develop the concept of the derivative, by looking for a reciprocal operation.

  • Aim 1: Know and apply the concepts of the definite and indefinite integral
  • Aim 2: Interpret the definite and indefinite integral geometrically
  • Aim 3: Find relations between the problems of calculating areas and antiderivatives using Barrow's rule.
  • Aim 4: Use the integral in basic geometric applications to calculate areas

   Enrique Martínez Arcos
Spanish Ministry of Education and Education. Year 2001

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