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Definite Integrals

Definite Integrals

Definite Integrals: Summation Domination True or False

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

2. Partial values of the function g 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 g and the x-axis on the interval [1,8].

-> 47

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
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].
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 .25 of the exact area of R? -> more than 3
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]? ->


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].

->


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)

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
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.

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