March 2012
Intermediate to advanced
604 pages
23h 58m
English
Content preview from Engineering Mathematics, Volume I, Second Edition
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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 ...
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