(1 point) You want to estimate the area underneath the graph of a positive funct

Question

(1 point) You want to estimate the area underneath the graph of a positive function by using rectangles of equal width. Check each True statements below: A. The absolute value of the Midpoints estimate is half of the absolute value of Trapezoid Rule estimate B. The absolute value of the error of the Midpoints estimate is about half of the absolute value of the error of the Trapezoid Rule estimate C. The Midpoint estimate is the average of the Left and Right endpoints estimates D. To use the Simpson's rule, an even number of rectangles must be used E. For an increasing function the Left endpoints estimate is an under-estimate and the Right end points estimate is an over-estimate

Explanation / Answer

From the given choices, Choice C and E are correct.

Because midpoint sum is average value of left end point sum and right end point sum.

And

IF function is increasing , then left end point sum is less than midpoint sum and midpoint sum is less than right end point sum.

Hence, left end point sum is underestimate and right end point sum is over estimate.

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