take a look at
http://www.math.pitt.edu/~sparling/052/23052/23052notes/23052notestojan14th/node3.html
In the case of a decreasing, concave down parabola in the intervals 0 to 1 with all of the y values positive, would the actual area be less or more than the estimated area using the trapezoid rule? And would it be less or more than using the midpoint rule? I know the left endpoint rectangles would give the highest area and the right endpoints would give the lowest, but I'm not sure about the others.
2 answers
The trapezoid rule gives more accurate estimate of the actual area. For that curve, on the left side of max, it give too high, on the right side, to low . Those areas ought to balance out.