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.
