Answer
69/8
Work Step by Step
If there are four intervals, we know that there must be four midpoints between zero and two. Therefore the midpoints will be x = 1/4, 3/4, 5/4, and 7/4. We can then plug those x’s into f(x) to get f(x) = 49/16, 57/16, 73/16, and 97/16 respectively. To perform midpoint rule we do the change in x times the f(x) of the x in between them for each midpoint, so (1/2-0)*f(1/4) + (1-1/2)*f(3/4) + (3/2-1)*f(5/4) + (2-3/2)*f(7/4) which equals 69/8.
