Question 1

Use integration tables to find  . ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

E

Question 2

Find the indefinite integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

D

Question 3

Use the Trapezoidal Rule to estimate the number of square meters of land in a lot where x and y are measured in meters as shown in the figure below. The land is bounded by a stream and two straight roads that meet at right angles. ​
​

​
A) 88,450
B) 88,250
C) 87,950
D) 88,950
E) 88,650

Accepted Answer

A

Question 4

Find the indefinite integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral. 
A) 
B) 
C)...

Question 5

Find the indefinite integral by making the substitution  . 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral by making the...

Question 6

Find the definite integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the definite integral. 
A) 
B) 
C)...

Question 7

Use the error formula to estimate the error in approximating the integral  with  using Simpson's Rule. Round your answer to six decimal places. ​
A) 0.003341
B) 0.023613
C) 0.001312
D) 0.010495
E) 0.031484

Accepted Answer

The answer of Use the error formula to estimate the...

Question 8

Use Simpson's Rule with  to approximate  using the equation  . Round your answer to five decimal places. ​
A) 3.14159
B) 3.13645
C) 3.14673
D) 3.14381
E) 3.13937

Accepted Answer

The answer of Use Simpson's Rule with  to approximate...

Question 9

Use integration tables to find the integral  . ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use integration tables to find the integral...

Question 10

Find the indefinite integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral. 
A) 
B) 
C)...

Question 11

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 16 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral. ​  ​
A) The Trapezoidal rule gives 5.008090 and Simpson's rule gives 5.258495.
B) The Trapezoidal rule gives -5.008090 and Simpson's rule gives -5.008382.
C) The Trapezoidal rule gives 5.008090 and Simpson's rule gives 5.008382.
D) The Trapezoidal rule gives 5.007217 and Simpson's rule gives 5.258495.
E) The Trapezoidal rule gives 5.007217 and Simpson's rule gives 5.008382.

Accepted Answer

The answer of Apply the Trapezoidal Rule and Simpson's Rule...

Question 12

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 10 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral. ​  ​
A) The Trapezoidal rule gives 13.7000 and Simpson's rule gives 14.3588.
B) The Trapezoidal rule gives 13.7000 and Simpson's rule gives 13.6667.
C) The Trapezoidal rule gives -13.6750 and Simpson's rule gives -13.6667.
D) The Trapezoidal rule gives 13.6750 and Simpson's rule gives 13.6667.
E) The Trapezoidal rule gives 13.6750 and Simpson's rule gives 14.3588.

Accepted Answer

The answer of Apply the Trapezoidal Rule and Simpson's Rule...

Question 13

Find the indefinite integral by making the substitution  . 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral by making the...

Question 14

Suppose a damping force affects the vibration of a spring so that the displacement of the string is given by  . Find the average value of y on the interval from  to  . Round your answer to three decimal places.
A) 1.000
B) 0.286
C) 0.255
D) 0.318
E) 0.800

Accepted Answer

The answer of Suppose a damping force affects the vibration...

Question 15

Find the indefinite integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral. 
A) 
B) 
C)...

Question 16

Solve  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Solve  .
A) 
B) 
C) 
D) 
E)...

Question 17

Find the indefinite integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral. 
A) 
B) 
C)...

Question 18

Determine whether the improper integral  diverges or converges. Evaluate the integral if it converges.
A) 
B) 
C) 
D) 
E) diverges

Accepted Answer

The answer of Determine whether the improper integral  diverges...

Question 19

Find the definite integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the definite integral. 
A) 
B) 
C)...

Question 20

Determine whether the improper integral  diverges or converges. Evaluate the integral if it converges.
A) 
B) 
C) 
D) 
E) diverges

Accepted Answer

The answer of Determine whether the improper integral  diverges...

Quiz 8: Integration Techniques and Improper Integrals

Use integration tables to find . ​

Find the indefinite integral.

Use the Trapezoidal Rule to estimate the number of square meters of land in a lot where x and y are measured in meters as shown in the figure below. The land is bounded by a stream and two straight roads that meet at right angles. ​ ​ ​

Find the indefinite integral.

Find the indefinite integral by making the substitution .

Find the definite integral.

Use the error formula to estimate the error in approximating the integral with using Simpson's Rule. Round your answer to six decimal places. ​

Use Simpson's Rule with to approximate using the equation . Round your answer to five decimal places. ​

Use integration tables to find the integral . ​

Find the indefinite integral.

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 16 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral. ​ ​

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 10 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral. ​ ​

Find the indefinite integral by making the substitution .

Suppose a damping force affects the vibration of a spring so that the displacement of the string is given by . Find the average value of y on the interval from to . Round your answer to three decimal places.

Find the indefinite integral.

Solve .

Find the indefinite integral.

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

Find the definite integral.

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

Use integration tables to find .

Use the Trapezoidal Rule to estimate the number of square meters of land in a lot where x and y are measured in meters as shown in the figure below. The land is bounded by a stream and two straight roads that meet at right angles.

Use the error formula to estimate the error in approximating the integral with using Simpson's Rule. Round your answer to six decimal places.

Use Simpson's Rule with to approximate using the equation . Round your answer to five decimal places.

Use integration tables to find the integral .

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 16 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 10 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.