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.
Let P(x, y) and Q(x+δx, y+δy) be two neighboring points on the given curve. Draw PR and QS perpendiculars ...
Get Engineering Mathematics, Volume I, Second Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
