The approximation rule alike to the Trapezoid Rule is the Midpoint Rule. The rule gives the approximation for the integral f(t)dt by (b a)([b+a]/2). Present a rigorous proof assuming the function f : [a, b] R is continuous and that its restriction : (a, b) R has a 2nd derivative, then for a point & (a,b), + - (b a)" (p) 1 24 = (b a)/2, n = (a+b)/2, & let G(t) = [fm+z ] 2x(n) ( 2 ) fn+% 25 ()n for xo x xo, then use - Tip: Let x = [*(t)dt = (b a)(+b) 2 Generalized Rolle's Theorem having m = 1 to the function G : [-o, To] R