Lab #4 Integration Trapezoidal Rule and Simpson's Rule Graph the following function in Mathematica: f(x) -x2+2x + 8, on the interval [-4, 6] Use the Trapezoidal Rule and Simpson's Rule give approximations to the integral: f(x)dx a Trapezoidal Rule f(x)dx f(xo) +2f(xi) + 2f(2) + 2f(x3) +. + 2f(xn-1+fx) and n is the number of equally spaced intervals [a, b] is split up on. where h =-, The error for this approximation is:--f" (),where [a,b]. Write a program to sum the areas of the trapezoids to approximate the actual area under the (b-a) iI 12n2 curve from -2 to 4, with h 0.5 Lab #4 Integration Trapezoidal Rule and Simpson's Rule Graph the following function in Mathematica: f(x) -x2+2x + 8, on the interval [-4, 6] Use the Trapezoidal Rule and Simpson's Rule give approximations to the integral: f(x)dx a Trapezoidal Rule f(x)dx f(xo) +2f(xi) + 2f(2) + 2f(x3) +. + 2f(xn-1+fx) and n is the number of equally spaced intervals [a, b] is split up on. where h =-, The error for this approximation is:--f" (),where [a,b]. Write a program to sum the areas of the trapezoids to approximate the actual area under the (b-a) iI 12n2 curve from -2 to 4, with h 0.5