Definite Integrals: Graphically
Consider the graph of f(x) (not f '(x)) below. Find the value of the definite integrals (a) through (f).
(a)
1
∫ f(x) dx
0
 (b)
2
∫ f(x) dx
1
 (c)
2
∫ f(x) dx
0
 (d)
3
∫ f(x) dx
2½
 (e)
4
∫ f(x) dx
3
 (f)
6
∫ f(x) dx
4

(g) If f(x) were the velocity function for the motion of an object (and x stood for time) what happened to the object between x=2 and x=3? Discuss the acceleration function a(x), and draw its graph below.