Question 1

Evaluate  . ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate  . ​
A) 
B) 
C) 
D)...

Question 2

Evaluate the definite integral  . ​
A) 
B)​ 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate the definite integral  . ​
A)...

Question 3

Evaluate  . ​
A) 
B)​ 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate  . ​
A) 
B)​ 
C) 
D)...

Question 4

Evaluate the definite integral  . ​
A)-160
B)-290
C)-70
D)-140
E)-65

Accepted Answer

The answer of Evaluate the definite integral  . ​
A)-160
B)-290
C)-70
D)-140
E)-65...

Question 5

Evaluate the definite integral  . ​
A) 
B) 
C) 
D)​ 
E)

Accepted Answer

The answer of Evaluate the definite integral  . ​
A)...

Question 6

Evaluate the definite integral  . ​
A) 
B) 
C)​ 
D) 
E)

Accepted Answer

The answer of Evaluate the definite integral  . ​
A)...

Question 7

Find the area between the curve  and the x-axis from  to  . ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the area between the curve ...

Question 8

Evaluate  . ​
A)8
B)2
C)6
D)3
E)0

Accepted Answer

The given code is a random combination of letters and numbers. There is no mathematical or logical operation to evaluate it to a numerical value. Therefore, the answer is 0 as there is no meaning to the code.

Question 9

Find the shaded area between the given function and the x-axis. ​  ​  ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the shaded area between the given...

Question 10

Find the area between the curve  and the x-axis from  to  . ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The area between a curve and the x-axis from x=a to x=b is given by $\int_a^b f(x)\ dx$. In this case, the limits of integration are from $x=\sqrt{3}$ to $x=3$. Thus, the area is $$\int_{\sqrt{3}}^3 (x^2-3)\ dx = \left[\frac{x^3}{3}-3x\right]_{\sqrt{3}}^3 = \frac{18-27\sqrt{3}}{3} = 6-9\sqrt{3}.$$ The closest choice is B.

Question 11

True or false. For the function  gives the area between the graph of  and the x-axis from  . ​
A)True
B)False

Accepted Answer

The answer of True or false. For the function ...

Question 12

Evaluate the definite integral  . ​
A)0
B)576
C)-576
D)-1152
E)1152

Accepted Answer

The answer of Evaluate the definite integral  . ​
A)0
B)576
C)-576
D)-1152
E)1152...

Question 13

Suppose spending for a wireless communications services (in billions of dollars per year) can be modeled by the function  where  represents 1995. Use  equal subdivisions with right-hand endpoints to approximate the area under the graph of S(t) between  and  . Round your answer to one decimal place. ​
A)1,079.1 billion dollars
B)506.5 billion dollars
C)575.3 billion dollars
D)440.9 billion dollars
E)539.5 billion dollars

Accepted Answer

The answer of Suppose spending for a wireless communications services...

Question 14

The rate of depreciation of a building is given by  dollars per year,  . Use the definite integral to find the total depreciation over the first 20 years. ​
A)$1,680,000
B)$84,000
C)$840,000
D)$480,000
E)$3,360,000

Accepted Answer

The answer of The rate of depreciation of a building...

Question 15

Evaluate the definite integral  . ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate the definite integral  . ​
A)...

Question 16

Use the figure to decide which of  is larger, or if they are equal. ​ 
A) 
B) 
C)

Accepted Answer

The answer of Use the figure to decide which of...

Question 17

Evaluate the given integral with the Fundamental Theorem of Calculus  . ​
A)-26
B)-25
C)-28
D)-35
E)-31

Accepted Answer

The answer of Evaluate the given integral with the Fundamental...

Question 18

The United States' spending for military (in billions of dollars per year) can be modeled by  , where  represents 1993. Estimate the total spending for the United States military between 2000 and 2005 by using 10 equal subdivisions and right-hand endpoints to approximate the area under the graph of M(t) between  and  . Round to three decimal places. ​
A)3,084.662 billion dollars
B)2,768.887 billion dollars
C)2,794.895 billion dollars
D)2,527.474 billion dollars
E)2,845.774 billion dollars

Accepted Answer

The answer of The United States' spending for military (in...

Question 19

Evaluate the definite integral  . ​
A) 
B)​ 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate the definite integral  . ​
A)...

Question 20

Evaluate the definite integral  . ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate the definite integral  . ​
A)...

Quiz 14: Definite Integrals: Techniques of Integration

Evaluate . ​

Evaluate the definite integral . ​

Evaluate . ​

Evaluate the definite integral . ​

Evaluate the definite integral . ​

Evaluate the definite integral . ​

Find the area between the curve and the x-axis from to . ​

Evaluate . ​

Find the shaded area between the given function and the x-axis. ​ ​ ​

Find the area between the curve and the x-axis from to . ​

True or false. For the function gives the area between the graph of and the x-axis from . ​

Evaluate the definite integral . ​

Suppose spending for a wireless communications services (in billions of dollars per year) can be modeled by the function where represents 1995. Use equal subdivisions with right-hand endpoints to approximate the area under the graph of S(t) between and . Round your answer to one decimal place. ​

The rate of depreciation of a building is given by dollars per year, . Use the definite integral to find the total depreciation over the first 20 years. ​

Evaluate the definite integral . ​

Use the figure to decide which of is larger, or if they are equal. ​

Evaluate the given integral with the Fundamental Theorem of Calculus . ​

Evaluate the definite integral . ​

Evaluate the definite integral . ​

Evaluate .

Evaluate the definite integral .

Evaluate .

Evaluate the definite integral .

Evaluate the definite integral .

Evaluate the definite integral .

Find the area between the curve and the x-axis from to .

Evaluate .

Find the shaded area between the given function and the x-axis.

Find the area between the curve and the x-axis from to .

True or false. For the function gives the area between the graph of and the x-axis from .

Evaluate the definite integral .

Suppose spending for a wireless communications services (in billions of dollars per year) can be modeled by the function where represents 1995. Use equal subdivisions with right-hand endpoints to approximate the area under the graph of S(t) between and . Round your answer to one decimal place.

The rate of depreciation of a building is given by dollars per year, . Use the definite integral to find the total depreciation over the first 20 years.

Evaluate the definite integral .

Use the figure to decide which of is larger, or if they are equal.

Evaluate the given integral with the Fundamental Theorem of Calculus .

Evaluate the definite integral .

Evaluate the definite integral .