5. First show that JI f(x) dx = 0 for all subintervals I of [a, b].

8.

(a) Notice that IXj - xj-11 :S IIPII for each j = 1,2, ... , n.

5.2 Riemann Sums 597 1.

(a) 1/4.

(b) 7ra2/4.

(c) 9.

(d) (3/2)(b2 - a2 ) + (b - a). (Note: If a ~ -1/3 or b:S -1/3, the integral represents the area of a trapezoid; if a < -1/3 <

b, the integral represents the difference of the areas of two triangles, one above the x axis and the other below the x axis.)

3. Do not forget that f is bounded.

5.

(b) You may use the fact that J xn dx = xn+l /(n + 1).