1. Arc Length … x y a b xi ... Pi P0 P1 Pna b xi
... Pi P0 P1 Pn
Curve C defined by y=f(x) – continuous on [a,b]

2. Length L of C:
If f(x) – continuous, then by Mean Value Th,

3. Approximate integration
Divide an interval [a,b] into n subintervals of width x,
then the integral can be approximated by Riemann sum:
Left end point approximation
Right end point approximation
Midpoint Rule
Average of Left and Right end point approximation 
Trapezoidal Rule

4. Error = amount that has to be added in order to make an approximation exact.Ln Rn Tn Mn 5 10 20 n EL ER ET EM 5 10 20
Error Bounds:

5. Approximation by parabola on each segment [xi,xi+2] (n - even) a b xi P2 P0 P1 Pn
xi+2
xi+1
Simpson’s Rule
Error Bound: