5. To evaluate a definite integral of tabular function f(x), piecewise quadratic approximation led to a. Trapezoidal Method b. Simpsons Rule

The correct option is;

b. Simpsons Rule

Step-by-step explanation:

The midpoint rule involves the estimation of the area under the curve with the aid of rectangular shaped approximations

The trapezoidal rule, involved the approximation of the curve by linear approximations by using piece by piece linear functions

In the Simpson's rule the curve is approximated using piece by piece quadratic functions. The intervals are partitioned into even numbered smaller intervals having the same width and we approximate the resulting integrals of the intervals.