consider the region bounded by f(x)= -x^2+x+6 and the x-axis. partiton into n rectangles of equal width, using their right endpoints to find their height. What is the summation that gives the area of these n rectangles?
I experimented with a much simpler problem to start with.
I let f(x)=2x
and found the area from x=2 to x=7 (above the x axis) using 4 strips
Then I went on to find n strips
then I was ready to tackle your problem
f(x)=-(x-3)(x+2) This is a concave down parabola that crosses the x axis at 3 and -2
The width of each strip is (3--2)/n = 5/n (where n is the the number of rectangles)
The right end point of each rectangle is x= -2 + (5/k) Where k can be any integer from 1 to n
The height
h = -(-2 + (5/k)-3)(-2 + (5/k)+2)
h = -(-5+(5/k))(5/k)
h = 5/k (5-5/k)
Area of each rectangle = 5/n * 5/k (5-5/k)
Area = The sum of k from 1 to n of [ 5/n * 5/k (5-5/k) ]
Area = The sum of k from 1 to n of [ (25/n*k) (5-5/k) ]
I think this is right but you had best check it very carefully.
I haven't actually plugged any numbers in to check that it works but if you divide the area into five rectangles you could see if it works for that quite easily.
If it doesn't work or you get stuck, post again, I should see you post easily enough.
+118654 
