9. Newton-Cotes formulas for evaluating abf(x)dx were based on polynomial approximations of f(x). Show that if y=f(x) is approximated by a natural cubic spline with evenly spaced knots at x0,x1,,xn, the quadrature formula becomes I=2h(y0+2y1+2y2++2yn1+yn)24h3(k0+2k1+k2++2kn1+kn) where h is the distance between the knots and ki=yi. Note that the first part is the composite trapezoidal rule; the second part may be viewed as a "correction" for curvature. 9. Newton-Cotes formulas for evaluating abf(x)dx were based on polynomial approximations of f(x). Show that if y=f(x) is approximated by a natural cubic spline with evenly spaced knots at x0,x1,,xn, the quadrature formula becomes I=2h(y0+2y1+2y2++2yn1+yn)24h3(k0+2k1+k2++2kn1+kn) where h is the distance between the knots and ki=yi. Note that the first part is the composite trapezoidal rule; the second part may be viewed as a "correction" for curvature