Question 1

Find the indefinite integral and check the result by differentiation. ​   ​

Accepted Answer

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

Question 2

Find the integral   . ​

Accepted Answer

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

Question 3

Find the general solution of the differential equation below and check the result by differentiation. ​   ​

Accepted Answer

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

Question 4

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

Accepted Answer

A)    
B)    
C)    
D)    
E)  2 
A)    
B)    
C)    
D)    
E)  2

Question 5

Evaluate the definite integral of the function. ​   ​
Use a graphing utility to verify your results.
​

Accepted Answer

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

Question 6

The maker of an automobile advertises that it takes 8 seconds to accelerate from 15 kilometers per hour to 70 kilometers per hour. Assuming constant acceleration, compute the distance, in meters, the car travels during the 8 seconds. Round your answer to two decimal places. ​

Accepted Answer

A)  49.50 m 
B)  188.89 m 
C)  94.44 m 
D)  97.78 m 
E)  61.11 m 
A)  49.50 m 
B)  188.89 m 
C)  94.44 m 
D)  97.78 m 
E)  61.11 m

Question 7

Find the limit. ​   ​

Accepted Answer

A)  4 
B)  10 
C)  20 
D)  16 
E)  8 
A)  4 
B)  10 
C)  20 
D)  16 
E)  8

Question 8

Find   . ​

Accepted Answer

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

Question 9

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral. ​   ​

Accepted Answer

A)  63 
B)  31.5 
C)  6 
D)  87 
E)  -43.5 
A)  63 
B)  31.5 
C)  6 
D)  87 
E)  -43.5

Question 10

Evaluate   and   in that order. ​

Accepted Answer

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

Question 11

Find the indefinite integral   . ​

Accepted Answer

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

Question 12

Find the indefinite integral   . ​

Accepted Answer

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

Question 13

Use the properties of summation and Theorem 5.2 to evaluate the sum. ​   ​

Accepted Answer

A)  395 
B)  18,759 
C)  18,629 
D)  6,357 
E)  18,603 
A)  395 
B)  18,759 
C)  18,629 
D)  6,357 
E)  18,603

Question 14

Find the integral   . ​

Accepted Answer

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

Question 15

Evaluate the definite integral. ​   ​

Accepted Answer

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

Question 16

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

Accepted Answer

A)  -36 
B)  -114 
C)  4 
D)  -146 
E)  -60 
A)  -36 
B)  -114 
C)  4 
D)  -146 
E)  -60

Question 17

Find the indefinite integral of the following function and check the result by differentiation. ​   ​

Accepted Answer

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

Question 18

Find the solution of the differential equation   which passes through the point   . ​

Accepted Answer

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

Question 19

Find the derivative of the function   . ​

Accepted Answer

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

Question 20

Find the indefinite integral of the following function and check the result by differentiation. ​   ​

Accepted Answer

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

Find the indefinite integral and check the result by differentiation.

Find the integral .

Find the general solution of the differential equation below and check the result by differentiation.

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

Evaluate the definite integral of the function. Use a graphing utility to verify your results.

The maker of an automobile advertises that it takes 8 seconds to accelerate from 15 kilometers per hour to 70 kilometers per hour. Assuming constant acceleration, compute the distance, in meters, the car travels during the 8 seconds. Round your answer to two decimal places.

Find the limit.

Find .

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

Evaluate and in that order.

Find the indefinite integral .

Find the indefinite integral .

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Find the integral .

Evaluate the definite integral.

Evaluate the integral. Given, , , , .

Find the indefinite integral of the following function and check the result by differentiation.

Find the solution of the differential equation which passes through the point .

Find the derivative of the function .

Find the indefinite integral of the following function and check the result by differentiation.

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

Find the indefinite integral and check the result by differentiation. ​ ​

Find the integral . ​

Find the general solution of the differential equation below and check the result by differentiation. ​ ​

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

Evaluate the definite integral of the function. ​ ​ Use a graphing utility to verify your results. ​

The maker of an automobile advertises that it takes 8 seconds to accelerate from 15 kilometers per hour to 70 kilometers per hour. Assuming constant acceleration, compute the distance, in meters, the car travels during the 8 seconds. Round your answer to two decimal places. ​

Find the limit. ​ ​

Find . ​

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral. ​ ​

Evaluate and in that order. ​

Find the indefinite integral . ​

Find the indefinite integral . ​

Use the properties of summation and Theorem 5.2 to evaluate the sum. ​ ​

Find the integral . ​

Evaluate the definite integral. ​ ​

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

Find the indefinite integral of the following function and check the result by differentiation. ​ ​

Find the solution of the differential equation which passes through the point . ​

Find the derivative of the function . ​

Find the indefinite integral of the following function and check the result by differentiation. ​ ​

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

Find the indefinite integral and check the result by differentiation.

Find the integral .

Find the general solution of the differential equation below and check the result by differentiation.

Evaluate the definite integral of the function. Use a graphing utility to verify your results.

The maker of an automobile advertises that it takes 8 seconds to accelerate from 15 kilometers per hour to 70 kilometers per hour. Assuming constant acceleration, compute the distance, in meters, the car travels during the 8 seconds. Round your answer to two decimal places.

Find the limit.

Find .

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

Evaluate and in that order.

Find the indefinite integral .

Find the indefinite integral .

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Find the integral .

Evaluate the definite integral.

Evaluate the integral. Given, , , , .

Find the indefinite integral of the following function and check the result by differentiation.

Find the solution of the differential equation which passes through the point .

Find the derivative of the function .

Find the indefinite integral of the following function and check the result by differentiation.