Approximate the area between the curve 
and the x-axis on the interval [0,2] using 4 rectangles and ...
(a) left sums
(b) right sums
(c) midpoint sums
Difficulty:
(a) Each interval will have a width of 
,
beginning at x = 0. Multiply the function value of the left-hand endpoint
of each interval times the width of the interval and add the results together:
(b) Follw the same procedure, this time using the height the function reaches at the right endpoint of each interval of width 1/2. For grins, I factored out the common width from each term and wrote it out front. It makes everything look a little neater.
(c) This time, you'll use the function's value at the midpoint of each interval.
For example the first interval of the four is 
,
which has a midpoint of 
:
