Answer
1.006
Work Step by Step
Since we know there must be four intervals (n=4) there are 4 midpoints from 0 to pi/2. So the midpoints are pi/16, 3pi/16, 5pi/16, and 7pi/16. We can then plug these into f(x) and get f(x) = 0.9808, 0.8315, 0.5555, and 0.1951 respectively. To apply midpoint rule we multiple the change in x by the f(x) of the middle x, so: (pi/8 - 0)*f(pi/16) + (pi/4 - pi/8)*f(3pi/16) + (3pi/8 - pi/4)*f(5pi/16) + (pi/2 - 3pi/8)*f(7pi/16) which = 1.006
