Consider the following. time left... 6 ( x 2 - 2x ) dx 1: 49 : 14 (a) Find an approximation to the integral using a Riemann sum with right endpoints and n = 8. R8 = (b) Draw a diagram to illustrate the approximation in part (a). U NW A N W 2 3 NIN NIC 3 NIS 5 NIC 4 2 2 -2 DO-3 N W A UI Q V OO LY NWAVIA NIC 3 2 5 3 2 NIN NIC -1 2 4 2 3 5 -2 (c) Consider the following theorem. If f is integrable on [a, b], then f(x) dx = ,"_ = lim (x,) Ax, where Ax = D - 2 and x, = a + iAx. 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. y 10 8 w H N WAUON 2 3 AUNL 2 3 HNW A U Q V OO O K HNWAU 3 -2 -2