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Problem 1 : Understanding of Discretization of Variables and Iterations Consider the summation of the square of a continuous function f ( x ) :

Problem 1: Understanding of Discretization of Variables and Iterations
Consider the summation of the square of a continuous function f(x) :
y=i=1k|f(x)|2
where x is a vector of length k defined as a set of evenly-spaced values from a to b, i.e., in MATLAB we define: x=1 inspace (a,b,k) and k=1,2,3,dots, etc.
a) Develop a numerical solver (i.e., function) to execute the above algorithm and determine the maximum number of terms in the summation before it exceeds a user-specified value ymax. The solver should have the following input/output structure.
function [y,N]= SquaredFunctionSum(fun,a,b,ymax )
where, the output N is the maximum number of terms in the series such that the sum does not exceed ymax.
b) Test your developed numerical solver on the function f(x)=x3 with inputs a=1,b=3, ymax=1000.
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