The width of each rectangle is found by taking the difference between the endpoints and
dividing by n. Here, the width of each rectangle is
We find the heights of the rectangles by evaluating y = 2x^3 at the appropriate endpoints:
; y(1) = 2 + (1)^3 = 3; ; y(2) = 2 +
(2)^3 = 10; ; y(3) = 2+(3)^3 = 29.
Therefore, the area is = .
10.
We find the average value of the function, f(x), on the interval [a, b] using the formula f(c) =
f(x) dx. Here we are looking for the average value of f(x) = on the interval
[−1, 1]. Using the formula, we need to find dx. We get
