The function f (x) = e^−x can be used to generate the following table of unequally spaced data:

Evaluate the integral from a = 0 to b = 0.6 using 

(a) Analytical means, 

(b) The trapezoidal rule, and 

(c) A combination of the trapezoidal and Simpson’s rules wherever possible to attain the highest accuracy. For (b) and (c), compute the true percent relative error.

X 0 0.1 0.3 0.5 0.7 f(x) 1 0.9048 0.7408 0.6065 0.4966 0.3867 0.95 1.2 0.3012