Unless specified, all approximating rectangles are assumed to have the same width.

Evaluate the upper and lower sums for

8 (9 - 8x) dx 0(c) Consider the following theorem. b If f is integrable on [a, b], then f(x) dx = lim f(x, ) Ax , where Ax = b- and X; = a + iAx. a n - co n i=1 Use this to evaluate the integral. (d) Interpret the integral in part (c) as a difference of areas. O The integral represents the area above the x-axis minus the area below the x-axis. O The integral represents the area below the x-axis minus the area above the x-axis. Illustrate with a diagram