Question 1

Evaluate the integral   . ​

Accepted Answer

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

Question 2

Evaluate the following definite integral. ​   ​
Use a graphing utility to check your answer.
​

Accepted Answer

A)    
B)    
C)  -1 
D)  1 
E)  0 
A)    
B)    
C)  -1 
D)  1 
E)  0

Question 3

Find the limit of   as   . ​   ​

Accepted Answer

A)  1/5 
B)  4 
C)  0 
D)  unbounded 
E)  8/5 
A)  1/5 
B)  4 
C)  0 
D)  unbounded 
E)  8/5

Question 4

Find the area of the region bounded by the graphs of the equations   , and   . Round your answer to four decimal places. ​

Accepted Answer

A)  8.5917 
B)  10.3178 
C)  9.5917 
D)  11.3178 
E)  9.6903 
A)  8.5917 
B)  10.3178 
C)  9.5917 
D)  11.3178 
E)  9.6903

Question 5

Evaluate the integral. ​   ​
Given,
​   ,   ,   ,   .
​

Accepted Answer

A)  -102 
B)  102 
C)  868 
D)  12 
E)  7,395 
A)  -102 
B)  102 
C)  868 
D)  12 
E)  7,395

Question 6

Evaluate the integral   . ​

Accepted Answer

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

Question 7

Find an equation of the tangent line to the graph of the function   at the point   . ​

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. ​   ​

Accepted Answer

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

Question 10

Find   . ​

Accepted Answer

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

Question 11

Evaluate the integral   . ​

Accepted Answer

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

Question 12

Apply the Extended Mean Value Theorem to the functions   and   on the interval   , and find all values c in the interval   such that   . ​

Accepted Answer

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

Question 13

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 14

Find the area of the shaded region for the function   . ​   ​

Accepted Answer

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

Question 15

Solve the differential equation. ​   ​

Accepted Answer

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

Question 16

Evaluate the limit   using L'Hopital's Rule if necessary. ​

Accepted Answer

A)  1 
B)    
C)  0 
D)    
E)    
A)  1 
B)    
C)  0 
D)    
E)

Question 17

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 18

Write the following limit as a definite integral on the interval [2, 4], where   is any point in the   subinterval. ​   ​

Accepted Answer

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

Question 19

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 20

The oscillating current in an electrical circuit is   where I is measured in amperes and t is measured in seconds. Find the average current for the time interval   . Round your answer to three decimal places.

Accepted Answer

A)  1.624 amps 
B)  0.624 amps 
C)  1.247 amps 
D)  2.494 amps 
E)  2.247 amps 
A)  1.624 amps 
B)  0.624 amps 
C)  1.247 amps 
D)  2.494 amps 
E)  2.247 amps

Evaluate the integral .

Evaluate the following definite integral. Use a graphing utility to check your answer.

Find the limit of as .

Find the area of the region bounded by the graphs of the equations , and . Round your answer to four decimal places.

Evaluate the integral. Given, , , , .

Evaluate the integral .

Find an equation of the tangent line to the graph of the function at the point .

Find the indefinite integral.

Find the indefinite integral.

Find .

Evaluate the integral .

Apply the Extended Mean Value Theorem to the functions and on the interval , and find all values c in the interval such that .

Find the indefinite integral.

Find the area of the shaded region for the function .

Solve the differential equation.

Evaluate the limit using L'Hopital's Rule if necessary.

Find the indefinite integral.

Write the following limit as a definite integral on the interval [2, 4], where is any point in the subinterval.

Find the indefinite integral.

The oscillating current in an electrical circuit is where I is measured in amperes and t is measured in seconds. Find the average current for the time interval . Round your answer to three decimal places.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

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 5: Integration

Evaluate the integral . ​

Evaluate the following definite integral. ​ ​ Use a graphing utility to check your answer. ​

Find the limit of as . ​ ​

Find the area of the region bounded by the graphs of the equations , and . Round your answer to four decimal places. ​

Evaluate the integral. ​ ​ Given, ​ , , , . ​

Evaluate the integral . ​

Find an equation of the tangent line to the graph of the function at the point . ​

Find the indefinite integral. ​ ​

Find the indefinite integral. ​ ​

Find . ​

Evaluate the integral . ​

Apply the Extended Mean Value Theorem to the functions and on the interval , and find all values c in the interval such that . ​

Find the indefinite integral. ​ ​

Find the area of the shaded region for the function . ​ ​

Solve the differential equation. ​ ​

Evaluate the limit using L'Hopital's Rule if necessary. ​

Find the indefinite integral. ​ ​

Write the following limit as a definite integral on the interval [2, 4], where is any point in the subinterval. ​ ​

Find the indefinite integral. ​ ​

The oscillating current in an electrical circuit is where I is measured in amperes and t is measured in seconds. Find the average current for the time interval . Round your answer to three decimal places.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

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

Evaluate the integral .

Evaluate the following definite integral. Use a graphing utility to check your answer.

Find the limit of as .

Find the area of the region bounded by the graphs of the equations , and . Round your answer to four decimal places.

Evaluate the integral. Given, , , , .

Evaluate the integral .

Find an equation of the tangent line to the graph of the function at the point .

Find the indefinite integral.

Find the indefinite integral.

Find .

Evaluate the integral .

Apply the Extended Mean Value Theorem to the functions and on the interval , and find all values c in the interval such that .

Find the indefinite integral.

Find the area of the shaded region for the function .

Solve the differential equation.

Evaluate the limit using L'Hopital's Rule if necessary.

Find the indefinite integral.

Write the following limit as a definite integral on the interval [2, 4], where is any point in the subinterval.

Find the indefinite integral.