Another way to think about the column Ia in Table 4.4.1 is to think that the value of the function is approximated by the average of the values at the beginning and the end of the time interval. We pretend that the rate of change is f(ti+1) + f(ti) / 2 during the interval from ti to ti+1. Use this method to estimate the following integrals. In each case,
a. Draw a graph illustrating the estimate.
b. Write an expression for Ia using summation notation.
c. Compute the sum.
f(t) = l + t3, limits of integration 0 to 1, n = 5.