(1 poii) You want to estimate the area underneath the graph of a positive functi

Question

(1 poii) 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 Midpoint estimate is the average of the Left and Right endpoints estimates C. To use the Simpson's rule, an even number of rectangles must be used D. 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 ?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

(A)

mid point = (a+b)/2

trapezoid =(a+b)/2

both are same

so, option-A is FALSE

(B)

Mid-point= (a+b)/2

a= left

b=right

so, option-B is true

(C)

yes... Simpson's rule is applied for even number of n

so, option-C is true

(D)

FALSE

(E)

TRUE

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