(Solved): matlab a) Use the Simpson's \( 3 / 8 \) rule with a single application of Simpson's \( 1 / 3 \) rule ...

a) Use the Simpson's \( 3 / 8 \) rule with a single application of Simpson's \( 1 / 3 \) rule at the end of the domain to integrate the function \[ f(x)=10-\sqrt{1+\left(x^{4} / 6800\right)^{2}} \] between 0 and 20 using 20 points. Provide your answer accurate to 4 decimal places. b) Integrate \( f(x) \) again over the domain \( 0 \leq x \leq 20 \) using the Trapezoidal rule with 20 points and provide the answer accurate to 4 decimal places. c) What is the minimum number of points required for a composite application composed of Simpson's \( 1 / 3 \) rule plus Simpson's \( 3 / 8 \) rule.