Asked by Ernie

Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integral from 0 to 2 of x squared, dx .
Answered by Steve
a few seconds with google will turn up several good online calculators for this and similar problems. You can use them to verify your results.
Answered by Ernie
What does it mean by "upper and lower estimates?"
How do I find these?
Answered by Steve
Of the left and right sums, one will overestimate and the other will underestimate.

Since the area of a trapezoid (with vertical bases h1 and h2) is (h1+h2)*w
You can see how that is the average of the left-side height and the right-side height for each sub-interval.

I can't believe this is not explained in your text, and in far greater detail, giving illustrations!
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