Question

If three equal subdivisions of [-4, 2] are used, find the trapezoidal approximation of integral of (e^(-x))/2 dx from -4 to 2.

Answer 1

Well the area of a trapezoid is

A = h/2(a + b) a and b are the parallel sides

in this question the a and b values become f(x) values

h is the height... or the distance between the x values



well start by using a table of values and dividing the interval into 3 equal parts..

this gives the height of each trapezoid h = 2

x : -4 : -2 : 0 : 2
-----------:--------:-------:---------
f(x) (e^4)/2 : (e^2)/2 : 1/2 : (e^-2)/2

then find the area of each trapezoid

A = [2/2(f(-4) + f(-2)] + [2/2(f(-2) + f(0)] + [2/2(f(0) + f(2)]

there is a formula that can be applied, but for 3 trapezoids its easier just to find the area of each and then sum the areas for the approximation of the integral

hope it helps