Question 1

Use Riemann sums and a limit to compute the exact area under the curve.   on

Accepted Answer

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

Question 2

Use the given substitution to evaluate the indicated integral.

Accepted Answer

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

Question 3

Evaluate the integral by computing the limit of Riemann sums.

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

Use Part 1 of the Fundamental Theorem of Calculus to compute the integral exactly.

Accepted Answer

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

Question 6

Sketch a graph of a function   corresponding to the given graph of   .

Accepted Answer

Answers may vary. On

Question 7

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

Accepted Answer

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

Question 8

Make the indicated substitution for an unspecified function   .   for

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Find the area above the   -axis and below   .

Accepted Answer

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

Question 11

Find all functions satisfying the given conditions.

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Find the derivative   .

Accepted Answer

A)  cos 4x2 - 5 
B)  2x(cos 4x2 - 5) 
C)  -sin 4x2 
D)  -2sin 4x2 
A)  cos 4x2 - 5 
B)  2x(cos 4x2 - 5) 
C)  -sin 4x2 
D)  -2sin 4x2

Question 14

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 15

Use the Integral Mean Value Theorem to estimate the value of the integral. Round to three decimal places, if necessary.

Accepted Answer

A)  between 0 and 36 
B)  between 1 and 9 
C)  between 4 and 36 
D)  between 0 and 9 
A)  between 0 and 36 
B)  between 1 and 9 
C)  between 4 and 36 
D)  between 0 and 9

Question 16

Approximate the given value using Simpson's Rule with   . Round to 3 decimal places.

Accepted Answer

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

Question 17

Find the position function   from the given velocity function and initial value. Assume that units are feet and seconds.

Accepted Answer

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

Question 18

Use the given function values to estimate the area under the curve using left-endpoint and right-endpoint evaluation. Round to two decimal places.   0.0

Accepted Answer

A)  Left-endpoint estimate is   ; right-endpoint estimate is   
B)  Left-endpoint estimate is   ; right-endpoint estimate is   
C)  Left-endpoint estimate is   ; right-endpoint estimate is   
D)  Left-endpoint estimate is   ; right-endpoint estimate is   
A)  Left-endpoint estimate is   ; right-endpoint estimate is   
B)  Left-endpoint estimate is   ; right-endpoint estimate is   
C)  Left-endpoint estimate is   ; right-endpoint estimate is   
D)  Left-endpoint estimate is   ; right-endpoint estimate is

Question 19

Determine the position function if the acceleration function is   , the initial velocity is   , and the initial position is   .

Accepted Answer

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

Question 20

Find the function   satisfying the given conditions.

Accepted Answer

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

Use Riemann sums and a limit to compute the exact area under the curve. on

Use the given substitution to evaluate the indicated integral.

Evaluate the integral by computing the limit of Riemann sums.

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

Use Part 1 of the Fundamental Theorem of Calculus to compute the integral exactly.

Sketch a graph of a function corresponding to the given graph of .

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

Make the indicated substitution for an unspecified function . for

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

Find the area above the -axis and below .

Find all functions satisfying the given conditions.

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

Find the derivative .

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

Use the Integral Mean Value Theorem to estimate the value of the integral. Round to three decimal places, if necessary.

Approximate the given value using Simpson's Rule with . Round to 3 decimal places.

Find the position function from the given velocity function and initial value. Assume that units are feet and seconds.

Use the given function values to estimate the area under the curve using left-endpoint and right-endpoint evaluation. Round to two decimal places. 0.0

Determine the position function if the acceleration function is , the initial velocity is , and the initial position is .

Find the function satisfying the given conditions.

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

Use Riemann sums and a limit to compute the exact area under the curve. on

Use the given substitution to evaluate the indicated integral.

Evaluate the integral by computing the limit of Riemann sums.

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

Use Part 1 of the Fundamental Theorem of Calculus to compute the integral exactly.

Sketch a graph of a function corresponding to the given graph of .

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

Make the indicated substitution for an unspecified function . for

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

Find the area above the -axis and below .

Find all functions satisfying the given conditions.

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

Find the derivative .

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

Use the Integral Mean Value Theorem to estimate the value of the integral. Round to three decimal places, if necessary.

Approximate the given value using Simpson's Rule with . Round to 3 decimal places.

Find the position function from the given velocity function and initial value. Assume that units are feet and seconds.

Use the given function values to estimate the area under the curve using left-endpoint and right-endpoint evaluation. Round to two decimal places. 0.0

Determine the position function if the acceleration function is , the initial velocity is , and the initial position is .

Find the function satisfying the given conditions.

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