The Midpoint and Trapezoid Sums Definition In a midpoint sum, we choose to compute the height of each rectangle in the center of each subinterval instead of on the left or right. 5. Fill in the blanks: . When we divide the interval [a, b] into n equal subintervals, the left hand of the ith subinterval is and its right hand is . So the center of the ith subinterval is The area of the ith rectangle in a midpoint sum is therefore Definition The trapezoid sum is the average of the left hand and right hand sums