In: Math
a) The following table gives the values of a function f(x) at a certain number of equidistant points on the x-axis. From the data supplied, calculate approximate values of by using each of the following rules: (Give the explicit formula/definition for each of the rules, before applying them)
(i) The Trapezoid Rule and (ii) Simpson's Rule.
| 
 x =  | 
 0.0  | 
 0.2  | 
 0.4  | 
 0.6  | 
 0.8  | 
 1.0  | 
 1.2  | 
 1.4  | 
 1.6  | 
 1.8  | 
 2.0  | 
| 
 f (x) =  | 
 2.7  | 
 2.1  | 
 2.3  | 
 1.7  | 
 2.2  | 
 2.9  | 
 3.1  | 
 3.4  | 
 3.9  | 
 4.9  | 
 8.7  | 
b) Use the Midpoint Rule to find the approximation to 6 decimal places.