Question 1

Find the indefinite integral.

Accepted Answer

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

Question 2

Use the given graph of   to find the Riemann sum with six subintervals. Take the sample points to be left endpoints.

Accepted Answer

A) 4 
B) 6 
C) 8 
D) 3.5 
E) 4.5 
A) 4 
B) 6 
C) 8 
D) 3.5 
E) 4.5

Question 3

Evaluate the Riemann sum for   ,   with four subintervals, taking the sample points to be right endpoints.

Accepted Answer

The answer of Evaluate the Riemann sum for  ...

Question 4

An animal population is increasing at a rate of   per year (where t is measured in years). By how much does the animal population increase between the fourth and tenth years?

Accepted Answer

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

Question 5

Find the general indefinite integral.

Accepted Answer

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

Question 6

Evaluate the integral.

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 7

Find the area of the region that lies under the given curve. Round the answer to three decimal places.

Accepted Answer

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

Question 8

Given that   , find   .

Accepted Answer

The answer of Given that   , find ...

Question 9

Find an expression for the area under the graph of   as a limit. Do not evaluate the limit.

Accepted Answer

The answer of Find an expression for the area under...

Question 10

Find the derivative of the function.

Accepted Answer

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

Question 11

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral.  ...

Question 12

Use the Midpoint Rule with n = 10 to approximate the integral.

Accepted Answer

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

Question 13

Evaluate the integral by making the given substitution.   ,

Accepted Answer

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

Question 14

Find the area of the region to three decimal places that lies under the given curve.

Accepted Answer

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

Question 15

Find the area of the region that lies to the right of the y-axis and to the left of the parabola   .

Accepted Answer

The answer of Find the area of the region that...

Question 16

Evaluate the integral by interpreting it in terms of areas.

Accepted Answer

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

Question 17

Express the limit as a definite integral on the given interval.

Accepted Answer

The answer of Express the limit as a definite integral...

Question 18

Find the interval on which the curve   is concave downward.

Accepted Answer

The answer of Find the interval on which the curve...

Question 19

Evaluate the indefinite integral.

Accepted Answer

The answer of Evaluate the indefinite integral.  ...

Question 20

The graph of a function f on the interval [0, 8] is shown in the figure. Compute the Riemann sum for f on [0, 8] using four subintervals of equal length and choosing the evaluation points to be (a) the left endpoints, (b) the right endpoints, and (c) the midpoints of the subintervals.

Accepted Answer

The answer of The graph of a function f on...

Find the indefinite integral.

Use the given graph of to find the Riemann sum with six subintervals. Take the sample points to be left endpoints.

Evaluate the Riemann sum for , with four subintervals, taking the sample points to be right endpoints.

An animal population is increasing at a rate of per year (where t is measured in years). By how much does the animal population increase between the fourth and tenth years?

Find the general indefinite integral.

Evaluate the integral.

Find the area of the region that lies under the given curve. Round the answer to three decimal places.

Given that , find .

Find an expression for the area under the graph of as a limit. Do not evaluate the limit.

Find the derivative of the function.

Evaluate the integral.

Use the Midpoint Rule with n = 10 to approximate the integral.

Evaluate the integral by making the given substitution. ,

Find the area of the region to three decimal places that lies under the given curve.

Find the area of the region that lies to the right of the y-axis and to the left of the parabola .

Evaluate the integral by interpreting it in terms of areas.

Express the limit as a definite integral on the given interval.

Find the interval on which the curve is concave downward.

Evaluate the indefinite integral.

The graph of a function f on the interval [0, 8] is shown in the figure. Compute the Riemann sum for f on [0, 8] using four subintervals of equal length and choosing the evaluation points to be (a) the left endpoints, (b) the right endpoints, and (c) the midpoints of the subintervals.

Functions and Limits

Derivatives

Applications of Differentiation

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

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Exam 4: Integrals

Find the indefinite integral.

Use the given graph of to find the Riemann sum with six subintervals. Take the sample points to be left endpoints.

Evaluate the Riemann sum for , with four subintervals, taking the sample points to be right endpoints.

An animal population is increasing at a rate of per year (where t is measured in years). By how much does the animal population increase between the fourth and tenth years?

Find the general indefinite integral.

Evaluate the integral.

Find the area of the region that lies under the given curve. Round the answer to three decimal places.

Given that , find .

Find an expression for the area under the graph of as a limit. Do not evaluate the limit.

Find the derivative of the function.

Evaluate the integral.

Use the Midpoint Rule with n = 10 to approximate the integral.

Evaluate the integral by making the given substitution. ,

Find the area of the region to three decimal places that lies under the given curve.

Find the area of the region that lies to the right of the y-axis and to the left of the parabola .

Evaluate the integral by interpreting it in terms of areas.

Express the limit as a definite integral on the given interval.

Find the interval on which the curve is concave downward.

Evaluate the indefinite integral.

The graph of a function f on the interval [0, 8] is shown in the figure. Compute the Riemann sum for f on [0, 8] using four subintervals of equal length and choosing the evaluation points to be (a) the left endpoints, (b) the right endpoints, and (c) the midpoints of the subintervals.

Functions and Limits

Derivatives

Applications of Differentiation

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters