Answer
0.345
Work Step by Step
Because we know we have 4 intervals, we must have 4 midpoint values. Therefore our midpoints are x = pi/32, 3pi/32, 5pi/32, and 7pi/32. We can then plug these values into f(x) and get f(x) = 0.0985, 0.3033, 0.5345, and 0.8207. We can then apply midpoint rule by multiplying the change in x by the f(x) of the x in the middle, so: (pi/16 - 0)*f(pi/32) + (pi/8 - pi/16)*f(3pi/32) + (3pi/16 - pi/8)*f(5pi/32) + (pi/4 - 3pi/16)*f(7pi/32) which = 0.345
