Question

We can easily improve the formula by approximating the area under the function f(x) by two equally-spaced trapezoids. Derive a formula for this approximation and implement it in a function trapezint2( f,a,b ).

Answer 1

Answer:

Explanation:

$\text{This is a math function that is integrated using a trapezoidal rule }$

$\text{import math}$

def $\text{trapezint2(f,a,b):}$

      $\text{midPoint=(a+b)/2}$

       $\text{return .5*((midPoint-a)*(f(a)+f(midPoint))+(b-midPoint)*(f(b)+f(midPoint)))}$

$\text{trapezint2(math.sin,0,.5*math.pi)}$

$0.9480594489685199$

$trapezint2(abs,-1,1)$

$1.0$