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Design two functions in C++ a) Utilizing the multiple application trapezoidal rule (h and a function to be integrated given by a table should be transferred there using function arguments); b) Utilizing the composite Simpson's rule (h and a function to be integrated given by a table should be transferred there using function arguments) 2. Apply two functions designed above to integrate the function f (x) given by the following table x f(x) 1.0 1.543 1.1 1.669 1.2 1.811 1.3 1.971 1.4 2.151 1.5 2.352 1.6 2.577 1.7 2.828 1.8 3.107 a) Using the multiple application trapezoidal rule with hsmall = 0.1 b) Using the multiple application Simpson's 1/3 rule with hsmall = 0.1; n = 8 3. Apply two functions designed above to integrate the function f (x) given by the following table x f(x) 1.0 1.543 1.1 1.669 1.3 1.971 1.4 2.151 1.5 2.352 1.7 2.828 1.8 3.107 c) Using the multiple application trapezoidal rule with hsmall = 0.1 d) Using the multiple application Simpson's 1/3 rule with hsmall = 0.1; n = 8 Use interpolation with a quadratic polynomial to find values of f (x) at missing points 1.2 and 1.6. Apply the Lagrangian method.