**Areas in Cartesian Co - ordinate :-**

Suppose we want to determine the area A1 bounded by the curve y = f(x) , the x - axis an two fixed ordinates x = a and x = b . The function f(x) , is supposed to be single - valued , finite and continuous in the interval (a , b ) .

The process of finding the area , bounded by any defined contour line is called

**Quadrature**,

**"the term meaning the investigation of the size of a square which shall have the same area as that of the region under consideration" .**

**Here are the example of some Plain Curves :-**

Name | Implicit equation | Parametric equation | As a function | graph | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Straight line | ||||||||||||||||||||

Circle | ||||||||||||||||||||

Parabola | ||||||||||||||||||||

Ellipse | ||||||||||||||||||||

Hyperbola |