Let's refer back to the graph used in the last section to answer the questions below:

1.- Find the integral of the function on the interval [-2,3] giving your answer to one decimal place. Write the answer in your exercise book. Then let a=3 and b=-2 and n remain invariable. What happens to your result? Repeat the same process with other pairs of values. Does the same thing always happen? Can you explain why? State the general property explaining what happens to an integral when we change round the order of the endpoints of the interval.

2.- Let a and b have the same value. What happens? Is this the case at any point where a and b are the same? State a general property for this case and explain why this happens.

Let's now take two functions, f(x) y g(x), which can be integrated on the same interval [a,b]. We now need to find out if the function f+g can also be integrated on this interval.

1.- Change the values of a and b and watch what happens to the sum of the integrals of f and g and the integral of f+g.

2.- State a general property about the integral of a sum of functions.

Now let's see what happens when the integral of a function is multiplied by a constant.

1.- Change the values of a, b and k and watch what happens to the values of k*(the integral of f) and (the integral of k*f).

2.- State the corresponding property which shows what happens to the integral of the product of a constant and a function.

Let's now see one last property of definite integrals.

1.- Change the value of c and watch what happens to the sum of integrals on the intervals [a,c] [c,b] and the integral on the interval [a,b].

2.- State the corresponding property.