posted by Yoona on .
Well, first graph the graph of f(x)=-1/10x^2 + 3
2. We are going to approximate the area between f and the x-axis from x = 0 to x = 4 using rectangles (the method of Riemann sums). This is not the entire area in the first quadrant, just most of it. Draw four inscribed rectangles of width 1 on the interval [0, 4] on you graph above.
3. What are the heights of each of the four rectangles? What is the total area of the rectangles? This area, although not the same as the area beneath the curve is an approximation for that area called the lower sum
4. The actual area between f and the x-axis on the interval [0, 4] is 28/3 . Why is one area greater?
5. How could you get a better approximation for the area beneath the curve if you still used inscribed rectangles?