Question 1

Sketch the area corresponding to the integral.

Accepted Answer

The answer of Sketch the area corresponding to the integral....

Question 2

Find the area between   and the x-axis for

Accepted Answer

A)  4 
B)  8 
C)    
D)    
A)  4 
B)  8 
C)    
D)

Question 3

Find the function   satisfying the given conditions.

Accepted Answer

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

Question 4

Find the derivative

Accepted Answer

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

Question 5

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

Accepted Answer

A)  1.000 
B)  0.020 
C)  0.750 
D)  0.667 
A)  1.000 
B)  0.020 
C)  0.750 
D)  0.667

Question 6

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 7

Find the area of the region bounded by   ,   , the x-axis, and the y-axis.

Accepted Answer

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

Question 8

Compute the error (the difference between the exact value and the approximation) in the Trapezoidal Rule approximation using   . Round to 5 decimal places.

Accepted Answer

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

Question 9

The location   of the center of gravity (balance point) of a flat plate bounded by   and the   -axis is given by   and   For the isosceles triangle bounded below by the   -axis and above by the function   (for   ), use symmetry to argue that   and   . Compute   .

Accepted Answer

@#IMG-DLM& . @#IMG-DLM& , since the integrand @#IMG-DLM& is

Question 10

Use the graph to determine whether   is positive or negative.

Accepted Answer

A)  Positive 
B)  Negative 
A)  Positive 
B)  Negative

Question 11

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

Accepted Answer

Answers may vary. On

Question 12

Suppose that a car can accelerate from   mph to   mph in   seconds. Assuming a constant acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the   seconds.

Accepted Answer

A)  Acceleration =   m/s22; distance =   miles 
B)  Acceleration =   m/s22; distance =   miles 
C)  Acceleration =   m/s22; distance =   miles 
D)  Acceleration =   m/s22; distance =   miles 
A)  Acceleration =   m/s22; distance =   miles 
B)  Acceleration =   m/s22; distance =   miles 
C)  Acceleration =   m/s22; distance =   miles 
D)  Acceleration =   m/s22; distance =   miles

Question 13

Suppose that a runner has velocity   mph for   minutes, velocity   mph for   minutes, velocity   mph for   minutes, and velocity   mph for   minutes. Find the distance run. 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

Find the general antiderivative.

Accepted Answer

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

Question 16

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)  58.704 
B)  70.381 
C)  63.000 
D)  61.698 
A)  58.704 
B)  70.381 
C)  63.000 
D)  61.698

Question 17

Find the derivative   .

Accepted Answer

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

Question 18

Use the graph to determine whether   is positive or negative.

Accepted Answer

A)  Positive 
B)  Negative 
A)  Positive 
B)  Negative

Question 19

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

Accepted Answer

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

Question 20

Suppose that a car can come to rest from   mph in   seconds. Assuming a constant (negative) acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the   seconds (i.e., the stopping distance).

Accepted Answer

A)  Acceleration =   m/s2; distance =   miles 
B)  Acceleration =   m/s2; distance =   miles 
C)  Acceleration =   m/s2; distance =   miles 
D)  Acceleration =   m/s2; distance =   miles 
A)  Acceleration =   m/s2; distance =   miles 
B)  Acceleration =   m/s2; distance =   miles 
C)  Acceleration =   m/s2; distance =   miles 
D)  Acceleration =   m/s2; distance =   miles

Sketch the area corresponding to the integral.

Find the area between and the x-axis for

Find the function satisfying the given conditions.

Find the derivative

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

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

Find the area of the region bounded by , , the x-axis, and the y-axis.

Compute the error (the difference between the exact value and the approximation) in the Trapezoidal Rule approximation using . Round to 5 decimal places.

The location of the center of gravity (balance point) of a flat plate bounded by and the -axis is given by and For the isosceles triangle bounded below by the -axis and above by the function (for ), use symmetry to argue that and . Compute .

Use the graph to determine whether is positive or negative.

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

Suppose that a car can accelerate from mph to mph in seconds. Assuming a constant acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the seconds.

Suppose that a runner has velocity mph for minutes, velocity mph for minutes, velocity mph for minutes, and velocity mph for minutes. Find the distance run. Round to two decimal places.

Evaluate the integral.

Find the general antiderivative.

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

Find the derivative .

Use the graph to determine whether is positive or negative.

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

Suppose that a car can come to rest from mph in seconds. Assuming a constant (negative) acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the seconds (i.e., the stopping distance).

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

Sketch the area corresponding to the integral.

Find the area between and the x-axis for

Find the function satisfying the given conditions.

Find the derivative

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

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

Find the area of the region bounded by , , the x-axis, and the y-axis.

Compute the error (the difference between the exact value and the approximation) in the Trapezoidal Rule approximation using . Round to 5 decimal places.

The location of the center of gravity (balance point) of a flat plate bounded by and the -axis is given by and For the isosceles triangle bounded below by the -axis and above by the function (for ), use symmetry to argue that and . Compute .

Use the graph to determine whether is positive or negative.

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

Suppose that a car can accelerate from mph to mph in seconds. Assuming a constant acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the seconds.

Suppose that a runner has velocity mph for minutes, velocity mph for minutes, velocity mph for minutes, and velocity mph for minutes. Find the distance run. Round to two decimal places.

Evaluate the integral.

Find the general antiderivative.

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

Find the derivative .

Use the graph to determine whether is positive or negative.

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

Suppose that a car can come to rest from mph in seconds. Assuming a constant (negative) acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the seconds (i.e., the stopping distance).

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