HARD CALCULUS PROBLEM

f(x)= 1/x

Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base (the midpoint rule), estimate the area under the graph of f(x) for x values between 1 and 5 using:

a.) Two rectangles:
Answer:

b.) Four rectangles:
Answer:





thanks

So midpoint rule given the function 1/x and for a 2 rectangles, therefore M2 is what we are solving for.

h = (5 - 1)/2 = 2 <-sub sections

Setting up a table of x values we get

x = 1 3 5
But since we are doing the midpoint rule the midpoints are 2 and 4
the corresponding y-values are 1/2 and 1/4 by subbing them in to 1/x

The midpoint rule states M2 = h(ymiddles)
Therefore = 2(1/2 + 1/4) = 6/4 = 3/2 Answer
similar can be done with four rectangles.