Definite Integrals Summation Domination True Or False

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1.	Use a left-hand sum with 3 sub-intervals to estimate the area between f (x) = \|x\| and the x-axis on the interval [-4, 2]. -> 12 True False
2.	Partial values of the function f are given in the table below. Use a left-hand sum with the sub-intervals suggested by the data in the table to estimate the area between the graph of f and the x-axis on the interval [1, 8]. -> 47 True False
3.	Determine which formula produces a right-hand sum approximation to the area between f and the x-axis on [1,10]. -> [f (2) + f (3) + f (4) + f (5) + f (6) + f (7) + f (8) + f (9)]Δ x True False
4.	Which of the following statements is true? -> If f is increasing on [a, b] then LHS(2) will provide an underestimate for the area between f and the x-axis on [a, b]. True False
5.	Let and let R be the region between the graph of f and the x-axis on [2, 4]. How many sub-intervals must we use to guarantee that the left-hand sum will be within 0.25 of the exact area of R? -> more than 3 True False
6.	Which picture best illustrates the area accounted for by using MID(3) to approximate the area between f (x) and the x-axis on [a, b]? -> True False
7.	Let f (x) = sin x + 1. Use a trapezoid sum with 4 sub-intervals to estimate the area between f and the x-axis on [0, 2π]. -> True False
8.	Partial values of the function f are shown in the table below. We want to estimate the area between f and the x-axis on [0, 4]. We can use the values in the table to find all but one of the following midpoint sums. Which midpoint sum cannot be found using the information in the table? -> MID(4) True False
9.	For which of the following functions f will any midpoint sum give an overestimate of the area between f and the x-axis on [0, 2]? -> f (x) = x² True False
10.	Let f be a non-negative function that is increasing and concave up. Let R be the region between the graph of f and the x-axis on [a, b]. Which of the following quantities is largest? -> The area of R. True False

Definite Integrals True or False

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