Solution for Problem 4

First, the students should recognize that since we only know the function values at the end points of each sub-interval, in order to apply the midpoint, we can only use half of our data and 5 sub-intervals rather than 10.

Input := 

Clear[y, i]

Input := 

dx = 1;
n = 10;
y[i_] = height[i];

Input := 

TrapRule10 =
	N[(dx/2) (y[0] + 2 Sum[y[i], {i, 1, n-1}] + y[n])]

Output =

57.8963

Input := 

SimpRule10 =
	N[(dx/3)
		(4 Sum[y[2 i - 1], {i, 1, n/2}] +
		 2 Sum[y[2 i], {i, 1, n/2 - 1}])]

Output =

58.2522