Question 1

Find the indefinite integral.

Accepted Answer

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

Question 2

Estimate the error in using (a) the Trapezoidal Rule and (b) Simpson's Rule with   when approximating the following integral. ​   ​

Accepted Answer

A)  The error for the Trapezoidal Rule is 0.0255 and for Simpson's Rule it is 0.0013. 
B)  The error for the Trapezoidal Rule is 0.0000 and for Simpson's Rule it is 0.0200. 
C)  The error for the Trapezoidal Rule is 0.1020 and for Simpson's Rule it is 0.0200. 
D)  The error for the Trapezoidal Rule is 0.1020 and for Simpson's Rule it is 0.0000. 
E)  The error for the Trapezoidal Rule is 0.0000 and for Simpson's Rule it is 0.0000. 
A)  The error for the Trapezoidal Rule is 0.0255 and for Simpson's Rule it is 0.0013. 
B)  The error for the Trapezoidal Rule is 0.0000 and for Simpson's Rule it is 0.0200. 
C)  The error for the Trapezoidal Rule is 0.1020 and for Simpson's Rule it is 0.0200. 
D)  The error for the Trapezoidal Rule is 0.1020 and for Simpson's Rule it is 0.0000. 
E)  The error for the Trapezoidal Rule is 0.0000 and for Simpson's Rule it is 0.0000.

Question 3

Find the area of the region bounded by the graphs of   , y = 0, x = 0, and x = 1.

Accepted Answer

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

Question 4

Find the indefinite integral.

Accepted Answer

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

Question 5

Find the indefinite integral.

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

Solve the differential equation   .

Accepted Answer

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

Question 8

Find the indefinite integral.

Accepted Answer

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

Question 9

Find the indefinite integral by making the substitution   . ​   ​

Accepted Answer

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

Question 10

Find the indefinite integral.

Accepted Answer

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

Question 11

Find   .

Accepted Answer

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

Question 12

Suppose a model for the ability M of a child to memorize, measured on a scale from 0 to10, is given by   where t is the child's age in years. Find the average value of this model between the child's first and second birthdays. Round your answer to three decimal places.

Accepted Answer

A)  2.209 
B)  0.892 
C)  1.734 
D)  5.059 
E)  3.750 
A)  2.209 
B)  0.892 
C)  1.734 
D)  5.059 
E)  3.750

Question 13

Evaluate the integral   . ​

Accepted Answer

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

Question 14

Use the error formula to estimate the error in approximating the integral   with   using Trapezoidal Rule. ​

Accepted Answer

A)  2 
B)  4 
C)  8 
D)  0 
E)  9 
A)  2 
B)  4 
C)  8 
D)  0 
E)  9

Question 15

Use a computer algebra system and Simpson's Rule with   to approximate t in the integral equation   . Round your answer to three decimal places. ​

Accepted Answer

A)  2.477 
B)  2.547 
C)  2.977 
D)  2.509 
E)  2.137 
A)  2.477 
B)  2.547 
C)  2.977 
D)  2.509 
E)  2.137

Question 16

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

Accepted Answer

A)  3.14159 
B)  3.13645 
C)  3.14673 
D)  3.14381 
E)  3.13937 
A)  3.14159 
B)  3.13645 
C)  3.14673 
D)  3.14381 
E)  3.13937

Question 17

Solve.

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

Find the definite integral.

Accepted Answer

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

Find the indefinite integral.

Estimate the error in using (a) the Trapezoidal Rule and (b) Simpson's Rule with when approximating the following integral.

Find the area of the region bounded by the graphs of , y = 0, x = 0, and x = 1.

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Solve the differential equation .

Find the indefinite integral.

Find the indefinite integral by making the substitution .

Find the indefinite integral.

Find .

Suppose a model for the ability M of a child to memorize, measured on a scale from 0 to10, is given by where t is the child's age in years. Find the average value of this model between the child's first and second birthdays. Round your answer to three decimal places.

Evaluate the integral .

Use the error formula to estimate the error in approximating the integral with using Trapezoidal Rule.

Use a computer algebra system and Simpson's Rule with to approximate t in the integral equation . Round your answer to three decimal places.

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

Solve.

Find the indefinite integral.

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

Find the definite integral.

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

Find the indefinite integral.

Estimate the error in using (a) the Trapezoidal Rule and (b) Simpson's Rule with when approximating the following integral. ​ ​

Find the area of the region bounded by the graphs of , y = 0, x = 0, and x = 1.

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Solve the differential equation .

Find the indefinite integral.

Find the indefinite integral by making the substitution . ​ ​

Find the indefinite integral.

Find .

Suppose a model for the ability M of a child to memorize, measured on a scale from 0 to10, is given by where t is the child's age in years. Find the average value of this model between the child's first and second birthdays. Round your answer to three decimal places.

Evaluate the integral . ​

Use the error formula to estimate the error in approximating the integral with using Trapezoidal Rule. ​

Use a computer algebra system and Simpson's Rule with to approximate t in the integral equation . Round your answer to three decimal places. ​

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

Solve.

Find the indefinite integral.

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

Find the definite integral.

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

Estimate the error in using (a) the Trapezoidal Rule and (b) Simpson's Rule with when approximating the following integral.

Find the indefinite integral by making the substitution .

Evaluate the integral .

Use the error formula to estimate the error in approximating the integral with using Trapezoidal Rule.

Use a computer algebra system and Simpson's Rule with to approximate t in the integral equation . Round your answer to three decimal places.

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