Question 1

Use Simpson's Rule with n = 4 steps to estimate the integral.
-

Accepted Answer

A)    
B)    
C)    
D)  81 
A)    
B)    
C)    
D)  81

Question 2

Evaluate the integral.
-

Accepted Answer

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

Question 3

Integrate the function.
-

Accepted Answer

A)  2   5 
B)  2   5 
C)  2     
D)    
A)  2   5 
B)  2   5 
C)  2     
D)

Question 4

Evaluate the improper integral or state that it is divergent.
-

Accepted Answer

A)  8   
B)  16 ln   
C)  16 ln 2 
D)  16 ln   
A)  8   
B)  16 ln   
C)  16 ln 2 
D)  16 ln

Question 5

Evaluate the integral.
-

Accepted Answer

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

Question 6

Evaluate the integral.
-

Accepted Answer

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

Question 7

Solve the problem.
-Suppose that the accompanying table shows the velocity of a car every second for 8 seconds. Use Simpson's Rule to approximate the distance traveled by the car in the 8 seconds. Round your answer to the nearest hundredth if necessary.

Accepted Answer

A)  168.33 ft 
B)  169.5 ft 
C)  170.33 ft 
D)  126 ft 
A)  168.33 ft 
B)  169.5 ft 
C)  170.33 ft 
D)  126 ft

Question 8

Use the Trapezoidal Rule with n = 4 steps to estimate the integral.
-

Accepted Answer

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

Question 9

Evaluate the integral.
-

Accepted Answer

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

Question 10

Give the appropriate form of the partial fraction decomposition.
-

Accepted Answer

A)    +   +   
B)    +   
C)    +   +   
D)    +   +   
A)    +   +   
B)    +   
C)    +   +   
D)    +   +

Question 11

Solve the problem.
-A rectangular swimming pool is being constructed, 18 feet long and 100 feet wide. The depth of the pool is measured at 3-foot intervals across the length of the pool. Estimate the volume of water in the pool using the Trapezoidal Rule.

Accepted Answer

A)  5800   
B)  7700   
C)  10,200   
D)  8700   
A)  5800   
B)  7700   
C)  10,200   
D)  8700

Question 12

Evaluate the improper integral or state that it is divergent.
-

Accepted Answer

A)  1.6667 
B)  1.3333 
C)  Divergent 
D)  2.6667 
A)  1.6667 
B)  1.3333 
C)  Divergent 
D)  2.6667

Question 13

Evaluate the integral.
-   dx

Accepted Answer

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

Question 14

Evaluate the integral by making a substitution and then using a table of integrals.
-

Accepted Answer

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

Question 15

Use reduction formulas to evaluate the integral.
-

Accepted Answer

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

Question 16

Integrate the function.
-

Accepted Answer

A)    + C 
B)    + C 
C)    + C 
D)    +   + C 
A)    + C 
B)    + C 
C)    + C 
D)    +   + C

Question 17

Express the integrand as a sum of partial fractions and evaluate the integral.
-   dx

Accepted Answer

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

Question 18

Solve the problem.
-Consider the region R bounded by the graph of f(x) =   on the interval [0, 3]. Find the volume of the solid formed when R is revolved about the x-axis.

Accepted Answer

A)    + 15 
B)    
C)    
D)    
A)    + 15 
B)    
C)    
D)

Question 19

Evaluate the integral.
- d $\theta$

Accepted Answer

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

Question 20

Evaluate the integral.
-

Accepted Answer

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

Use Simpson's Rule with n = 4 steps to estimate the integral. -

Evaluate the integral. -

Integrate the function. -

Evaluate the improper integral or state that it is divergent. -

Evaluate the integral. -

Evaluate the integral. -

Solve the problem. -Suppose that the accompanying table shows the velocity of a car every second for 8 seconds. Use Simpson's Rule to approximate the distance traveled by the car in the 8 seconds. Round your answer to the nearest hundredth if necessary.

Use the Trapezoidal Rule with n = 4 steps to estimate the integral. -

Evaluate the integral. -

Give the appropriate form of the partial fraction decomposition. - $Give the appropriate form of the partial fraction decomposition. -$

Solve the problem. -A rectangular swimming pool is being constructed, 18 feet long and 100 feet wide. The depth of the pool is measured at 3-foot intervals across the length of the pool. Estimate the volume of water in the pool using the Trapezoidal Rule.

Evaluate the improper integral or state that it is divergent. -

Evaluate the integral. - dx

Evaluate the integral by making a substitution and then using a table of integrals. -

Use reduction formulas to evaluate the integral. -

Integrate the function. -

Express the integrand as a sum of partial fractions and evaluate the integral. - $Express the integrand as a sum of partial fractions and evaluate the integral. - dx$ dx

Solve the problem. -Consider the region R bounded by the graph of f(x) = on the interval [0, 3]. Find the volume of the solid formed when R is revolved about the x-axis.

Evaluate the integral. - $Evaluate the integral. - d \theta$ d $\theta$

Evaluate the integral. -

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Exam 8: Integration Techniques

Use Simpson's Rule with n = 4 steps to estimate the integral. -

Evaluate the integral. -

Integrate the function. -

Evaluate the improper integral or state that it is divergent. -

Evaluate the integral. -

Evaluate the integral. -

Solve the problem. -Suppose that the accompanying table shows the velocity of a car every second for 8 seconds. Use Simpson's Rule to approximate the distance traveled by the car in the 8 seconds. Round your answer to the nearest hundredth if necessary.

Use the Trapezoidal Rule with n = 4 steps to estimate the integral. -

Evaluate the integral. -

Give the appropriate form of the partial fraction decomposition. -

Solve the problem. -A rectangular swimming pool is being constructed, 18 feet long and 100 feet wide. The depth of the pool is measured at 3-foot intervals across the length of the pool. Estimate the volume of water in the pool using the Trapezoidal Rule.

Evaluate the improper integral or state that it is divergent. -

Evaluate the integral. - dx

Evaluate the integral by making a substitution and then using a table of integrals. -

Use reduction formulas to evaluate the integral. -

Integrate the function. -

Express the integrand as a sum of partial fractions and evaluate the integral. - dx

Solve the problem. -Consider the region R bounded by the graph of f(x) = on the interval [0, 3]. Find the volume of the solid formed when R is revolved about the x-axis.

Evaluate the integral. -d θ\thetaθ

Evaluate the integral. -

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Give the appropriate form of the partial fraction decomposition. - $Give the appropriate form of the partial fraction decomposition. -$

Express the integrand as a sum of partial fractions and evaluate the integral. - $Express the integrand as a sum of partial fractions and evaluate the integral. - dx$ dx

Evaluate the integral. - $Evaluate the integral. - d \theta$ d $\theta$