1. 
Use a lefthand sum with 3 subintervals to estimate the area between f ( x ) = x and the xaxis on the interval [4,2]. > 12

2. 
Partial values of the function g are given in the table below. Use a lefthand sum with the subintervals suggested by the data in the table to estimate the area between the graph of g and the xaxis on the interval [1,8]. > 47

3. 
Determine which formula produces a righthand sum approximation to the area between f and the xaxis 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 xaxis on [a,b].

5. 
Let and let R be the region between the graph of f and the xaxis on [2,4]. How many subintervals must we use to guarantee that the lefthand 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 xaxis on [a,b]? >

7. 
Let f ( x ) = sin x + 1. Use a trapezoid sum with 4 subintervals to estimate the area between f and the xaxis 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 xaxis 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 xaxis on [0,2]? > f ( x ) = x^{2}

10. 
Let f be a nonnegative function that is increasing and concave up. Let R be the region between the graph of f and the xaxis on [a,b]. Which of the following quantities is largest? > The area of R.
