Question 1

Find an antiderivative by reversing the chain rule, product rule or quotient rule.

Accepted Answer

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

Question 2

Use a computer or calculator to compute the Simpson's Rule approximation with   . Round to 3 decimal places. Compare this value to the approximation given by your calculator.

Accepted Answer

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

Question 3

Use mathematical induction to prove that   for all integers   .

Accepted Answer

For @#IMG-DLM& , we have @#IMG-DLM& So,

Question 4

Use the Midpoint Rule to estimate the value of the integral (obtain two digits of accuracy).

Accepted Answer

A)  1.20 
B)    
C)  0.77 
D)  0.43 
A)  1.20 
B)    
C)  0.77 
D)  0.43

Question 5

List the evaluation points corresponding to the midpoint of each subinterval, and evaluate the corresponding Riemann sum. Round the sum to two decimal places.

Accepted Answer

A)  Evaluation points:   Riemann sum:   
B)  Evaluation points:   Riemann sum:   
C)  Evaluation points:   Riemann sum:   
D)  Evaluation points:   Riemann sum:   
A)  Evaluation points:   Riemann sum:   
B)  Evaluation points:   Riemann sum:   
C)  Evaluation points:   Riemann sum:   
D)  Evaluation points:   Riemann sum:

Question 6

List the evaluation points corresponding to the midpoint of each subinterval, sketch the function and corresponding approximating rectangles and evaluate the corresponding Riemann sum. Round the sum to two decimal places.

Accepted Answer

The evaluation point

Question 7

Use the Trapezoidal Rule to estimate   from the given data. Round to 2 decimal places.

Accepted Answer

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

Question 8

The velocity of an object at various times is given in the table below. Use the data to estimate the total distance traveled.

Accepted Answer

Using Simpson's Rule, we can e

Question 9

Write the given (total) area as an integral or sum of integrals. The area between   and the   -axis for   .

Accepted Answer

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

Question 10

Find an antiderivative by reversing the chain rule, product rule or quotient rule.

Accepted Answer

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

Question 11

Use the given substitution to evaluate the indicated integral.

Accepted Answer

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

Question 12

Evaluate the integral.

Accepted Answer

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

Question 13

Translate into summation notation.

Accepted Answer

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

Question 14

Use Part I of the Fundamental Theorem of Calculus to compute the integral exactly.

Accepted Answer

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

Question 15

Evaluate the indicated integral.

Accepted Answer

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

Question 16

Find the position function   from the given acceleration function and initial values. Assume that units are feet and seconds.

Accepted Answer

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

Question 17

The impulse-momentum equation states the relationship between a force   applied to an object of mass   and the resulting change in velocity   of the object. The equation is   , where   . Suppose that the force of a golf club on a ball is approximately   thousand pounds for   between 0 and   seconds. Using   slugs for the mass of a golf ball, estimate the change in velocity   (in ft/s). Round to 2 decimal places.

Accepted Answer

A)    ft/s 
B)    ft/s 
C)    ft/s 
D)    ft/s 
A)    ft/s 
B)    ft/s 
C)    ft/s 
D)    ft/s

Question 18

Compute the error (the difference between the exact value and the approximation) to 5 decimal places in each of the Midpoint, Trapezoidal and Simpson's Rule approximations using   .

Accepted Answer

A)  Midpoint error: 0.02033 Trapezoidal error: 0.12109
Simpson's error: 0.08048 
B)  Midpoint error: 0.00019 Trapezoidal error: 0.12109
Simpson's error: 0.08048 
C)  Midpoint error: 0.02033 Trapezoidal error: 0.00038
Simpson's error: 0.00000 
D)  Midpoint error: 0.00019 Trapezoidal error: 0.00038
Simpson's error: 0.00000 
A)  Midpoint error: 0.02033 Trapezoidal error: 0.12109
Simpson's error: 0.08048 
B)  Midpoint error: 0.00019 Trapezoidal error: 0.12109
Simpson's error: 0.08048 
C)  Midpoint error: 0.02033 Trapezoidal error: 0.00038
Simpson's error: 0.00000 
D)  Midpoint error: 0.00019 Trapezoidal error: 0.00038
Simpson's error: 0.00000

Question 19

Make the indicated substitution for an unspecified function   .   for

Accepted Answer

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

Question 20

Find the general antiderivative.

Accepted Answer

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

Find an antiderivative by reversing the chain rule, product rule or quotient rule.

Use a computer or calculator to compute the Simpson's Rule approximation with . Round to 3 decimal places. Compare this value to the approximation given by your calculator.

Use mathematical induction to prove that for all integers .

Use the Midpoint Rule to estimate the value of the integral (obtain two digits of accuracy).

List the evaluation points corresponding to the midpoint of each subinterval, and evaluate the corresponding Riemann sum. Round the sum to two decimal places.

List the evaluation points corresponding to the midpoint of each subinterval, sketch the function and corresponding approximating rectangles and evaluate the corresponding Riemann sum. Round the sum to two decimal places.

Use the Trapezoidal Rule to estimate from the given data. Round to 2 decimal places.

The velocity of an object at various times is given in the table below. Use the data to estimate the total distance traveled.

Write the given (total) area as an integral or sum of integrals. The area between and the -axis for .

Find an antiderivative by reversing the chain rule, product rule or quotient rule.

Use the given substitution to evaluate the indicated integral.

Evaluate the integral.

Translate into summation notation.

Use Part I of the Fundamental Theorem of Calculus to compute the integral exactly.

Evaluate the indicated integral.

Find the position function from the given acceleration function and initial values. Assume that units are feet and seconds.

Compute the error (the difference between the exact value and the approximation) to 5 decimal places in each of the Midpoint, Trapezoidal and Simpson's Rule approximations using .

Make the indicated substitution for an unspecified function . for

Find the general antiderivative.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 5: Integration

Find an antiderivative by reversing the chain rule, product rule or quotient rule.

Use a computer or calculator to compute the Simpson's Rule approximation with . Round to 3 decimal places. Compare this value to the approximation given by your calculator.

Use mathematical induction to prove that for all integers .

Use the Midpoint Rule to estimate the value of the integral (obtain two digits of accuracy).

List the evaluation points corresponding to the midpoint of each subinterval, and evaluate the corresponding Riemann sum. Round the sum to two decimal places.

List the evaluation points corresponding to the midpoint of each subinterval, sketch the function and corresponding approximating rectangles and evaluate the corresponding Riemann sum. Round the sum to two decimal places.

Use the Trapezoidal Rule to estimate from the given data. Round to 2 decimal places.

The velocity of an object at various times is given in the table below. Use the data to estimate the total distance traveled.

Write the given (total) area as an integral or sum of integrals. The area between and the -axis for .

Find an antiderivative by reversing the chain rule, product rule or quotient rule.

Use the given substitution to evaluate the indicated integral.

Evaluate the integral.

Translate into summation notation.

Use Part I of the Fundamental Theorem of Calculus to compute the integral exactly.

Evaluate the indicated integral.

Find the position function from the given acceleration function and initial values. Assume that units are feet and seconds.

Compute the error (the difference between the exact value and the approximation) to 5 decimal places in each of the Midpoint, Trapezoidal and Simpson's Rule approximations using .

Make the indicated substitution for an unspecified function . for

Find the general antiderivative.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters