9

Quadrature and Rectification

In this chapter, we discuss the processes to find area of a given bounded region of a curve and to find length of an arc of a curve between two given points. Of course, these concepts are nothing but applications of definite integral.

9.1 QUADRATURE

The process of finding the area of a bounded region of a curve is called quadrature.

9.1.1 Area of a Curve Given by the Cartesian Equation

Let AB be the arc of the curve y = f(x), between two ordinates x = a and x = b represented by AC and BD respectively.

 

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Let P(x, y) and Q(xx, yy) be two neighboring points on the given curve. Draw PR and QS perpendiculars ...

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