Question 1

Give an area interpretation of the integral.

Accepted Answer

Area between the fun

Question 2

Compute   , given

Accepted Answer

A)    
B)    
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D)    
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D)

Question 3

Write the expression as a single integral.

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D)

Question 4

For a business using just-in-time inventory, a delivery of 40 items arrives just as the last item is shipped out. Suppose that items are shipped out at a nonconstant rate such that   gives the number of items in inventory and t is measured in days. Find the time T at which the next shipment must arrive. Find the average value of f on the interval

Accepted Answer

@#IMG-DLM& days; ave

Question 5

Compute the Simpson's Rule approximation by hand for   . Round to 3 decimal places.

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Question 6

Evaluate the integral exactly.

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Question 7

Evaluate the integral.

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Question 8

Evaluate the definite integral.

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Question 9

Use the graph to estimate the Trapezoidal Rule approximation with   of   .

Accepted Answer

The answer of Use the graph to estimate the Trapezoidal...

Question 10

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

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Question 11

The table shows the velocity of a projectile at various times. Estimate the distance traveled. Round to two decimal places.

Accepted Answer

One estimate is give

Question 12

Find a function f (x) such that point (1, 2) is in the graph of y = f (x), the slope of the tangent line at (1, 2) is -5, and f ''(x) = x - 1

Accepted Answer

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B)    
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D)

Question 13

Use Simpson's Rule to estimate   from the given data. Round to 2 decimal places.

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Question 14

Estimate the integral numerically.

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D)      
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Question 15

Use summation rules to compute the sum.

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Question 16

If   is the angle between the path of a moving object and a fixed ray (see the figure below), the angular velocity of the object is   and the angular acceleration of the object is   .   Suppose a baseball batter rotates a bat through an angle of   with a constant angular acceleration of   rad/2s2. If the tip of the bat is located   feet from the pivot point (the batter's body), the (linear) speed of the tip of the bat is   . Find the value of   that will produce a speed of   mph for the tip of the bat at impact. Round to the nearest integer.

Accepted Answer

A)    rad/s2 
B)    rad/s2 
C)    rad/s2 
D)    rad/s2 
A)    rad/s2 
B)    rad/s2 
C)    rad/s2 
D)    rad/s2

Question 17

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

Accepted Answer

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

Question 18

Use a computer or calculator to compute the Midpoint, Trapezoidal and Simpson's Rule approximation with   . Round to 4 decimal places.

Accepted Answer

A)  Midpoint: 3.9779 Trapezoidal: 4.1841
Simpson's: 4.8784 
B)  Midpoint: 0.0990 Trapezoidal: 4.1841
Simpson's: 1.6893 
C)  Midpoint: 3.9779 Trapezoidal: 5.2345
Simpson's: 1.6893 
D)  Midpoint: 0.0990 Trapezoidal: 5.2345
Simpson's: 4.8784 
A)  Midpoint: 3.9779 Trapezoidal: 4.1841
Simpson's: 4.8784 
B)  Midpoint: 0.0990 Trapezoidal: 4.1841
Simpson's: 1.6893 
C)  Midpoint: 3.9779 Trapezoidal: 5.2345
Simpson's: 1.6893 
D)  Midpoint: 0.0990 Trapezoidal: 5.2345
Simpson's: 4.8784

Question 19

Find an equation of the tangent line at the given value of x.   , x = 3

Accepted Answer

A)  y = 2x + 6 
B)  y = 2x - 6 
C)  y = 3x - 9 
D)  y = 3x + 9 
A)  y = 2x + 6 
B)  y = 2x - 6 
C)  y = 3x - 9 
D)  y = 3x + 9

Question 20

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

Accepted Answer

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D)

Give an area interpretation of the integral.

Compute , given

Write the expression as a single integral.

Compute the Simpson's Rule approximation by hand for . Round to 3 decimal places.

Evaluate the integral exactly.

Evaluate the integral.

Evaluate the definite integral.

Use the graph to estimate the Trapezoidal Rule approximation with of .

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

The table shows the velocity of a projectile at various times. Estimate the distance traveled. Round to two decimal places.

Find a function f (x) such that point (1, 2) is in the graph of y = f (x), the slope of the tangent line at (1, 2) is -5, and f ''(x) = x - 1

Use Simpson's Rule to estimate from the given data. Round to 2 decimal places.

Estimate the integral numerically.

Use summation rules to compute the sum.

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

Use a computer or calculator to compute the Midpoint, Trapezoidal and Simpson's Rule approximation with . Round to 4 decimal places.

Find an equation of the tangent line at the given value of x. , x = 3

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

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

Give an area interpretation of the integral.

Compute , given

Write the expression as a single integral.

Compute the Simpson's Rule approximation by hand for . Round to 3 decimal places.

Evaluate the integral exactly.

Evaluate the integral.

Evaluate the definite integral.

Use the graph to estimate the Trapezoidal Rule approximation with of .

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

The table shows the velocity of a projectile at various times. Estimate the distance traveled. Round to two decimal places.

Find a function f (x) such that point (1, 2) is in the graph of y = f (x), the slope of the tangent line at (1, 2) is -5, and f ''(x) = x - 1

Use Simpson's Rule to estimate from the given data. Round to 2 decimal places.

Estimate the integral numerically.

Use summation rules to compute the sum.

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

Use a computer or calculator to compute the Midpoint, Trapezoidal and Simpson's Rule approximation with . Round to 4 decimal places.

Find an equation of the tangent line at the given value of x. , x = 3

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

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