For each of the following statements, determine whether it is true or false. If it is true, prove it. If it is false, give a counter example to disprove it.

(a) If f is an integrable function defined on [0,2] such that

2

f(t)dt = 4, then there exists a number c in the interval [0,2] such that f(c) = 2

0

(b) If a continuous variable force of average value 10 N on the interval 1x3 meters is applied to move an object along the x-axis from x = 1 to x = 3 meters, then the work done by the force in moving the object is 20 J.