Question 1

Evaluate the definite integral   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

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

Accepted Answer

A)    
B)    
C)    
D)    
E)  diverges 
A)    
B)    
C)    
D)    
E)  diverges

Question 3

Find the indefinite integral. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 4

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. ​
​

​

Accepted Answer

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

Question 5

Evaluate the integral   using the integration limits. Round your answer to three decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Find the indefinite integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Find the indefinite integral   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Use integration tables to evaluate the integral   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Use the Trapezoid Rule to approximate the value of the definite integral   with   . Round your answer to four decimal places.

Accepted Answer

A)  11.0000 
B)  8.5000 
C)  10.5000 
D)  9.0000 
E)  44.0000 
A)  11.0000 
B)  8.5000 
C)  10.5000 
D)  9.0000 
E)  44.0000

Question 10

Find the definite integral.

Accepted Answer

A)  12 
B)  6 
C)  2 
D)  102 
E)  1 
A)  12 
B)  6 
C)  2 
D)  102 
E)  1

Question 11

Find the indefinite integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

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. ​   ​

Accepted Answer

A)  The Trapezoidal rule gives 0.3400 and Simpson's rule gives 0.3398. 
B)  The Trapezoidal rule gives -0.3399 and Simpson's rule gives -0.3398. 
C)  The Trapezoidal rule gives 0.3400 and Simpson's rule gives 0.3569. 
D)  The Trapezoidal rule gives 0.3399 and Simpson's rule gives 0.3398. 
E)  The Trapezoidal rule gives 0.3399 and Simpson's rule gives 0.3569. 
A)  The Trapezoidal rule gives 0.3400 and Simpson's rule gives 0.3398. 
B)  The Trapezoidal rule gives -0.3399 and Simpson's rule gives -0.3398. 
C)  The Trapezoidal rule gives 0.3400 and Simpson's rule gives 0.3569. 
D)  The Trapezoidal rule gives 0.3399 and Simpson's rule gives 0.3398. 
E)  The Trapezoidal rule gives 0.3399 and Simpson's rule gives 0.3569.

Question 13

Find the indefinite integral by making the substitution   . ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Find the indefinite integral by making the substitution   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Use partial fractions to find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Find the indefinite integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

Find the indefinite integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

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

Accepted Answer

A)    
B)    
C)    
D)    
E)  diverges 
A)    
B)    
C)    
D)    
E)  diverges

Question 20

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.

Accepted Answer

A)  1.000 
B)  0.286 
C)  0.255 
D)  0.318 
E)  0.800 
A)  1.000 
B)  0.286 
C)  0.255 
D)  0.318 
E)  0.800

Evaluate the definite integral .

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

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.

Evaluate the integral using the integration limits. Round your answer to three decimal places.

Find the indefinite integral.

Find the indefinite integral .

Use integration tables to evaluate the integral .

Use the Trapezoid Rule to approximate the value of the definite integral with . Round your answer to four decimal places.

Find the definite integral.

Find the indefinite 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 .

Find the indefinite integral by making the substitution .

Find .

Use partial fractions to find $Use partial fractions to find .$ .

Find the indefinite integral.

Find the indefinite integral.

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

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.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 8: Integration Techniques and Improper Integrals

Evaluate the definite integral .

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

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. ​ ​ ​

Evaluate the integral using the integration limits. Round your answer to three decimal places.

Find the indefinite integral.

Find the indefinite integral .

Use integration tables to evaluate the integral . ​

Use the Trapezoid Rule to approximate the value of the definite integral with . Round your answer to four decimal places.

Find the definite integral.

Find the indefinite 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 . ​ ​

Find the indefinite integral by making the substitution .

Find .

Use partial fractions to find .

Find the indefinite integral.

Find the indefinite integral.

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

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.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

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.

Use integration tables to evaluate the 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 .

Use partial fractions to find $Use partial fractions to find .$ .

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