One other estimate of the integral, called Im, can be computed by pretending that the value during the interval from ti to ti+1 is the value of the function at the midpoint, or f[(ti+1 + ti)/2]. Use this method to estimate the following integrals. In each case,
a. Draw a graph illustrating this estimate for n = 5. Make sure you see the difference from Ia.
b. Write an expression for Im using summation notation.
c. Compute the sum.
f(t) = 2t, limits of integration 0 to 1, n = 5.