2. Simpson's rule. f(r)dx, with the given data set: Consider the Simpson's rule for the integral 0 0.00 0.250.50 0.75 1.00 f( 0.000.060.240.51 0.84 The plots of the derivatives of f are given below: 4th derivative 3rd derivative 1st derivative 2nd derivative 2.0 1.8 0.0 0.5 2.0 2.5 3.0 3.5 1.0 2.0 2.5 3.0 3.5 0.8 0.2 0.0 0.2 0.4 06 0.8 100.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 a). Compute the numerical integration using Simpson's rule with h - 0.25 (b) If the error tolerance is 10 6, how many points must one use for Simpson's rule with uniform grid