SOLUTION: Find the midpoint riemann sum for f(x) = cos(2x) on the partition P = {-pi/2,0,pi/3,pi/2} Please show how this is done Thank you

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Question 1003297: Find the midpoint riemann sum for f(x) = cos(2x) on the partition
P = {-pi/2,0,pi/3,pi/2}

Please show how this is done
Thank you
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
First sketch f(x) on the xy-plane and label the points (-pi/2, 0), (0,0), (0, pi/3), and (0,pi/2) (corresponding to the points in P).

To approximate the integral using the midpoint Riemann sum, for each "interval" bounded by consecutive points in P, take the midpoint and evaluate f at that x-value. This becomes your "height" of the rectangle. Multiply by the width of the interval.

For example, for the interval bounded by -pi/2, 0, we would want to take -pi/4 and compute f(-pi/4). Then we multiply f(-pi/4) by pi/2 (the width of the interval). Repeat for the other intervals and add.