Consider the function f(x) = x^2 + 2 on the closed interval [1, 6]. Using rectangles, use n = 10 and calculate the approximate area between the function f and the x axis on the interval [1, 5]. Use left endpoints in the following.
1. Find the change in x for each sub-interval.
2. Find f(1); f(1.5); f(2); f(2.5); f(3) . . . , f(5.5)
3. Find the area of each of the ten rectangles.
4. Find the sum of the areas of all ten rectangles to estimate the area under the curve.
This solution determines area and estimates with finite sums.