To approximate the arc length of a parametric curve on

some interval from $t=a$to $t=b$, we subdivide $[a,b]$

into n pieces to define $t_1=a,t_2,t_3,.....,t_n.$and consider the line segments connecting $\left(x\right(t_k-1),y(t_k-1\left)\right)$and $\left(x\right(t_k),y(t_k\left)\right)$for each $k=1,2,.....,n.$Define $∆x_k$

and $∆y_k$for the kth line segment in terms of the coordinates shown in the following figure:

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