How do the integral calculation to get the area of a circle? Lecture 1 part a of geometry

Lectures 1 part a of geometry.

Why not only open the mathematics handbooks or if you already know the formula which is A = pi*r^2.

   But let´s do something more interesting with the integral calculation for both Cartesian (rectangular coordinates) and polar coordinates.

 

1)      The integral calculation in Cartesian coordinates,

 

The first calculation

The half cicle which you get from the integral calculation

 

2)      The integral calculation in polar coordinates,

The second calculation

The first part of this lecture is over and for the next time we want to continue to calculate more area which comes from integrals over functions.

   Thereafter I want to do some rotation around axis integral calculations.