Lab #4 Integration Trapezoidal Rule and Simpson's Rule Graph the following function in Mathematica: f(x) --x22x 8, on the interval [-4,6]. Use the Trapezoidal Rule and Simpson's Rule give approximations to the integral: Ja f(x)dx a) Trapezoidal Rule f(x)dx * f(xo) 2f(x1) 2f(x2) 2f(x3) + +2f(xn-1) f(xn)), where h and n is the number of equally spaced intervals [a, b] is split up on. 7n The error for this approximation is: 1n" Write a program to sum the areas of the trapezoids to approximate the actual area under the curve from-2 to 4, with h 0.5. b) Simpson's Rule f(x)dxxo 4f(xi) 2f(x2) +4f(x3) 2f(x4)4f(xn-i) +f(xn)). where hand n is the number of equally spaced intervals [a, b] is split up on. The error for this approximation is: m (b-a) maxlf(4)(f)|,where E [a, b] Write a program to sum the areas under the interpolated curves to approximate the actual 72 180 area under the curve from-2 to 4, with h = 0.5