Problem 4: (Numerical Integration) Given: u(x)-f(x)+*K(x,t)u(t) dr (1) Where a and b and the function f and K are given. To approximate the function u on the interval [a, b]. a partition xa<<<<<<=b is selected and the equation: u(x) = f(x)+(x,t) n(t) dr. for each i=0... Are solved for u(x).(x)u(x). The integrals are approximated using quadrature formulas based on the nodes xxx. In this problem. a=0.b=1. f(x)=x². and K(x1)= a. Show that the linear system n(0) = f(0)+[* (0.0) (0)+(0.1)u(1)]: (1)= f(1)+[K (1.0)(0)+K (1.1)u(1)]: Must be solved when the Trapezoidal rule is used. (3) b. Set up and solve the linear system that results when Composite Simpson's rule is used with m=4, 6, 8. c. Plot on the same chart the approximation obtained for u(x) from part a and part b.