The table below gives selected values for the function f(x). With 5 rectangles, using the midpoint of each rectangle to evaluate the height of each rectangle, estimate...

Question

The table below gives selected values for the function f(x). With 5 rectangles, using the midpoint of each rectangle to evaluate the height of each rectangle, estimate the value of 

f(x)	1	0.909	0.833	0.769	0.714	0.667	0.625	0.588	0.556	0.526	0.500

X 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

A	0.7456
B	0.6456
C	0.6919
D	0.6932

Answer 1

If you divide the interval from 1 to 2 into 5 equal subintervals. each subinterval has a width of .2: (2-1)/5.

The left hand endpoint of the 1st subinterval will be 1 and the right hand endpoint 1.2. The midpoint of that sub interval will be 1.1: (1 + 1.2)/2.

Using that midpoint to calculate the height of the 1st rectangle is found as f(1.1) = .909.

The area of the 1st rectangle is given by f(1.1) (.2) [height time width], which is .1818.

Proceed in a similar fashion for the remaining four rectangles, adding the areas to get approximation for the total area.