Consider the integral i when answering the following questions.

1-Consider the given function.

Evaluate the Riemann sum for 2 ≤ x ≤ 14, with six subintervals, taking the sample points to be left endpoints.

L6 =

2-If

f(x) = 3x2 − 2x, 0 ≤ x ≤ 3,

evaluate the Riemann sum with n = 6, taking the sample points to be right endpoints.

R6 =

3-The graph of a function g is given.

a = 4

Consider the integral I when answering the following questions.

(a) Estimate the integral I with six subintervals using right endpoints.

R6 =

(b) Estimate the integral I with six subintervals using left endpoints.

L6 =

(c) Estimate the integral I with six subintervals using midpoints.

M6 =

4-The table gives the values of a function obtained from an experiment. Use them to estimate

9

f(x) dx

3

using three equal subintervals with right endpoints, left endpoints, and midpoints.

x

3

4

5

6

7

8

9

f(x)

−3.4

−2.2

−0.6

0.2

0.7

1.5

1.7

(a) Estimate

9

f(x) dx

3

using three equal subintervals with right endpoints.

R3 =

If the function is known to be an increasing function, can you say whether your estimate is less than or greater than the exact value of the integral?

less than

greater than

one cannot say

(b) Estimate

9

f(x) dx

3

using three equal subintervals with left endpoints.

L3 =

If the function is known to be an increasing function, can you say whether your estimate is less than or greater than the exact value of the integral?

less than

greater than

one cannot say

(c) Estimate

9

f(x) dx

3

using three equal subintervals with midpoints.

M3 =

If the function is known to be an increasing function, can you say whether your estimate is less than or greater than the exact value of the integral?

less than

greater than

one cannot say

5-Express the limit as a definite integral on the given interval.

lim

n →

n

[3 − 5(xi*)2 + 6(xi*)5] Δx, [4, 7]

i = 1

7

dx

4

6- (a)

6

g(x) dx

0

(b)

18

g(x) dx

6

(c)

21

g(x) dx

0

7-If

7

f(x) dx = 8

1

and

7

f(x) dx = 3.4,

5

find

5

f(x) dx.

1

8-If f is a continuous function, then the indefinite integral of f

precisely defines a function.

is a family of functions.

is a riddle, wrapped in a mystery, inside an enigma.

is a number.