Consider the following. ( " ( x 2 - 3x ) dx (a) Find an approximation to the integral using a Riemann sum with right endpoints and n = 8. Ra = | (b) Draw a diagram to illustrate the approximation in part (a). 3 3 3 2 2 2 2 1 1 1 X X X NID- 3 NIJ 4 5 NID- NIJ 4 5 2 3 4 5 NIJ NIJ 4 5 -1 -1 -1 -2 - 2 -2 10-3 10-3 (c) Consider the following theorem. If f is integrable on [a, b], then ( "Ax) dx - lim > Ax) AX, where AX - 5- 2 and x, = a + iAx. Use this to evaluate the integral.(c) Consider the following theorem. If f is integrable on [a, b], then ( A(x) dx - lim > now (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 below the x-axis minus the area above the x-axis. O The integral represents the area above the x-axis minus the area below the x-axis. Illustrate with a diagram. 4 6 3 5 3 3 2 N N 4 1 2 3 A 5 -1 N X 1 2 5 1 - 1 -1 X - 2 -2 1 2 3 4 0-5 10-1 @0-34 10-3