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.

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

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*+δ*x*, *y*+δ*y*) be two neighboring points on the given curve. Draw *PR* and *QS* perpendiculars ...

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