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 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
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 .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 ) = x^{2}
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