Question 1

Approximate the area under the curve on the given interval using   rectangles and right-endpoint evaluation. Round to three decimal places.   on   ,

Accepted Answer

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

Question 2

Compute the average value of the function on the given interval.

Accepted Answer

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

Question 3

The following table shows the acceleration of a car moving in a straight line. If the car is traveling   ft/s at time   , estimate the speed and distance traveled at each time.

Accepted Answer

Some estimates are given in the table be

Question 4

Compute the average value of the function on the given interval.

Accepted Answer

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

Question 5

Write the given (signed) area as an integral or sum of integrals. The area below the   -axis and above

Accepted Answer

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

Question 6

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 7

Find a value of   that satisfies the conclusion of the Integral Mean Value Theorem.

Accepted Answer

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

Question 8

Evaluate the integral.

Accepted Answer

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

Question 9

Compute the sum of the form   for the given function and   -values, with   equal to the difference in adjacent   's.   ;

Accepted Answer

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

Question 10

Evaluate the integral by computing the limit of Riemann sums.

Accepted Answer

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

Question 11

Use the given information about   and its derivatives to determine whether (a) the Midpoint Rule would be exact, underestimate or overestimate the integral (or if there's not enough information to tell). Repeat for (b) the Trapezoidal Rule and (c) Simpson's Rule.

Accepted Answer

Since @#IMG-DLM& , we have that @#IMG-DLM& is increasing, an

Question 12

Use formulas to compute the sum.

Accepted Answer

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

Question 13

Suppose that a car has velocity   mph for   hours, velocity   mph for   hours, velocity   mph for   minutes, and velocity   mph for   hours. Find the distance traveled. Round to two decimal places.

Accepted Answer

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

Question 14

Evaluate the integral.

Accepted Answer

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

Question 15

Write out all terms and compute the sum.

Accepted Answer

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

Question 16

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 17

Compute the Trapezoidal Rule approximation by hand for   . Round to 3 decimal places.

Accepted Answer

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

Question 18

Write out all terms and compute the sum.

Accepted Answer

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

Question 19

Translate the following calculation into summation notation and then compute the sum. The sum of the squares of the first   positive integers.

Accepted Answer

A)    
B)    
C)    
D)    sum =   
A)    
B)    
C)    
D)    sum =

Question 20

Use the given velocity function and initial position to estimate the final position s(b). Round to three decimal places, if necessary.   , s(0) = 0, b = 10

Accepted Answer

A)  2.998 
B)  2.305 
C)  2.308 
D)  2.402 
A)  2.998 
B)  2.305 
C)  2.308 
D)  2.402

Approximate the area under the curve on the given interval using rectangles and right-endpoint evaluation. Round to three decimal places. on ,

Compute the average value of the function on the given interval.

The following table shows the acceleration of a car moving in a straight line. If the car is traveling ft/s at time , estimate the speed and distance traveled at each time.

Compute the average value of the function on the given interval.

Write the given (signed) area as an integral or sum of integrals. The area below the -axis and above

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

Find a value of that satisfies the conclusion of the Integral Mean Value Theorem.

Evaluate the integral.

Compute the sum of the form for the given function and -values, with equal to the difference in adjacent 's. ;

Evaluate the integral by computing the limit of Riemann sums.

Use the given information about and its derivatives to determine whether (a) the Midpoint Rule would be exact, underestimate or overestimate the integral (or if there's not enough information to tell). Repeat for (b) the Trapezoidal Rule and (c) Simpson's Rule.

Use formulas to compute the sum.

Suppose that a car has velocity mph for hours, velocity mph for hours, velocity mph for minutes, and velocity mph for hours. Find the distance traveled. Round to two decimal places.

Evaluate the integral.

Write out all terms and compute the sum.

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

Compute the Trapezoidal Rule approximation by hand for . Round to 3 decimal places.

Write out all terms and compute the sum.

Translate the following calculation into summation notation and then compute the sum. The sum of the squares of the first positive integers.

Use the given velocity function and initial position to estimate the final position s(b). Round to three decimal places, if necessary. , s(0) = 0, b = 10

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

Approximate the area under the curve on the given interval using rectangles and right-endpoint evaluation. Round to three decimal places. on ,

Compute the average value of the function on the given interval.

The following table shows the acceleration of a car moving in a straight line. If the car is traveling ft/s at time , estimate the speed and distance traveled at each time.

Compute the average value of the function on the given interval.

Write the given (signed) area as an integral or sum of integrals. The area below the -axis and above

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

Find a value of that satisfies the conclusion of the Integral Mean Value Theorem.

Evaluate the integral.

Compute the sum of the form for the given function and -values, with equal to the difference in adjacent 's. ;

Evaluate the integral by computing the limit of Riemann sums.

Use the given information about and its derivatives to determine whether (a) the Midpoint Rule would be exact, underestimate or overestimate the integral (or if there's not enough information to tell). Repeat for (b) the Trapezoidal Rule and (c) Simpson's Rule.

Use formulas to compute the sum.

Suppose that a car has velocity mph for hours, velocity mph for hours, velocity mph for minutes, and velocity mph for hours. Find the distance traveled. Round to two decimal places.

Evaluate the integral.

Write out all terms and compute the sum.

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

Compute the Trapezoidal Rule approximation by hand for . Round to 3 decimal places.

Write out all terms and compute the sum.

Translate the following calculation into summation notation and then compute the sum. The sum of the squares of the first positive integers.

Use the given velocity function and initial position to estimate the final position s(b). Round to three decimal places, if necessary. , s(0) = 0, b = 10

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