Simpsons rule exact valueSolutionLet fx 4x a0 b8 By Trapezo

(Simpson\'s rule)

(exact value)

Solution

Let f(x) = 4x, a=0, b=8.

By Trapezoidal Rule, integral = (b-a)*(f(a)+f(b))/2 = (8*82)/2 = 322 = 45.2548

By Simpson\'s Rule, integral = (b-a)*(f(a) + 4f((a+b)/2) + f(b)) / 6

= 8 * ( 0 + 4*8 + 82 ) / 6

= 57.7516

Actual integral = 4 * 2 x^3/2/3 (with limit from 0 to 8)

= 4 * 2/3 * 162 = 60.3398

Note: As you can see, Simpson\'s Rule is more approximate.