Exam 5: Integration

The chief economist for a meat-packing plant estimates that if L worker-hours of labor are employed each week, the number of pounds of meat made ready for sale will be given by $Q ( L ) = 500 L^ { 3 / 4 }$ . Find the average weekly output as labor varies from 460 to 800 hours. Round to the nearest pound.

(Short Answer)

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Question 141

For the demand function $D ( q ) = \frac { 400 } { ( 0.2 q + 1 ) ^ { 2 } }$ dollars per unit, find the total amount of money consumer's are willing to spend when q = 3 units.

(Multiple Choice)

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Question 142

$\int 2 x \sqrt { x ^ { 2 } - 2 } d x = \frac { 2 \left( x ^ { 2 } - 2 \right) ^ { 3 / 2 } } { 3 } + C$

(True/False)

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Question 143

Given an initial population, $P _ { 0 } = 60,000$ , a renewal rate, R = 189, and a survival function, $S ( t ) = e ^ { - 0.05 t }$ , with time t measured in years, determine the population at the end of 11 years.

(Multiple Choice)

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Question 144

Evaluate $\int \left( x ^ { 3 } - 3 x ^ { 2 } + 5 \right) d x$ .

(Short Answer)

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Question 145

Evaluate $\int _ { - 1 } ^ { 1 } x ^ { 11 } d x$ .

(Multiple Choice)

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Question 146

Evaluate $\int \left( 1 - \frac { 3 } { x } + \frac { 5 } { x ^ { 3 } } \right) d x$ .

(Short Answer)

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Question 147

Evaluate $\int e ^ { 9 x - 6 } d x$ .

(Multiple Choice)

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Question 148

The slope $f ^ { \prime } ( x )$ at each point (x, y) on a curve y = f (x) is given, along with a particular point (a,b) on the curve. Use this information to find f (x).

(Multiple Choice)

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Question 149

Evaluate $\int _ { 2 } ^ { 3 } \frac { 3 x - 2 } { x ^ { 5 } } d x$ . Approximate to four decimal places.

(Short Answer)

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Question 150

Evaluate $\int \left( 4 x ^ { 7 } - e ^ { x } \right) d x$ .

(Short Answer)

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Question 151

Compute the area of the finite region bounded by the graphs of the functions $y = 5 x ^ { 2 }$ , and $y = - 5 x ^ { 2 } - 20 x + 80$

(Multiple Choice)

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Question 152

Find the average value of f (x) = 2x + 3 over the interval 0 $\le$ x $\le$ 5.

(Short Answer)

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Question 153

Evaluate $\int _ { - 1 } ^ { 1 } \frac { 5 } { \sqrt [ 3 ] { 2 x + 3 } } d x$ . Approximate your answer to two decimal places, if necessary.

(Multiple Choice)

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Question 154

Find the volume of the solid of revolution formed by rotating the region R about the x-axis.R is the region under the curve $y = \sqrt { 4 - x ^ { 2 } }$ from x = -2 to x = 2.

(Short Answer)

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Question 155

Evaluate $\int _ { - 1 } ^ { 1 } x ^ { 11 } d x$

(Multiple Choice)

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Question 156

Evaluate $\int \frac { x ^ { 5 } } { x ^ { 6 } + 3 } d x$ .

(Short Answer)

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Question 157

Evaluate $\int \left( 1 - \frac { 9 } { x } + \frac { 5 } { x ^ { 7 } } \right) d x$ .

(Short Answer)

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Question 158

Evaluate $\int \left( e ^ { 2 t } + e ^ { - 3 t } \right) d t$ .

(Short Answer)

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Question 159

Evaluate $\int x ^ { 6 } \sqrt { x ^ { 7 } + 4 } d x$

(Multiple Choice)

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Question 160

For the demand function $D ( q ) = \frac { 400 } { ( 0.2 q + 1 ) ^ { 2 } }$ dollars per unit, find the total amount of money consumer's are willing to spend when q = 3 units.

$\int 2 x \sqrt { x ^ { 2 } - 2 } d x = \frac { 2 \left( x ^ { 2 } - 2 \right) ^ { 3 / 2 } } { 3 } + C$

Given an initial population, $P _ { 0 } = 60,000$ , a renewal rate, R = 189, and a survival function, $S ( t ) = e ^ { - 0.05 t }$ , with time t measured in years, determine the population at the end of 11 years.

Evaluate $\int \left( x ^ { 3 } - 3 x ^ { 2 } + 5 \right) d x$ .

Evaluate $\int _ { - 1 } ^ { 1 } x ^ { 11 } d x$ .

Evaluate $\int \left( 1 - \frac { 3 } { x } + \frac { 5 } { x ^ { 3 } } \right) d x$ .

Evaluate $\int e ^ { 9 x - 6 } d x$ .

The slope $f ^ { \prime } ( x )$ at each point (x, y) on a curve y = f (x) is given, along with a particular point (a,b) on the curve. Use this information to find f (x).

Evaluate $\int _ { 2 } ^ { 3 } \frac { 3 x - 2 } { x ^ { 5 } } d x$ . Approximate to four decimal places.

Evaluate $\int \left( 4 x ^ { 7 } - e ^ { x } \right) d x$ .

Compute the area of the finite region bounded by the graphs of the functions $y = 5 x ^ { 2 }$ , and $y = - 5 x ^ { 2 } - 20 x + 80$

Find the average value of f (x) = 2x + 3 over the interval 0 $\le$ x $\le$ 5.

Evaluate $\int _ { - 1 } ^ { 1 } \frac { 5 } { \sqrt [ 3 ] { 2 x + 3 } } d x$ . Approximate your answer to two decimal places, if necessary.

Find the volume of the solid of revolution formed by rotating the region R about the x-axis.R is the region under the curve $y = \sqrt { 4 - x ^ { 2 } }$ from x = -2 to x = 2.

Evaluate $\int _ { - 1 } ^ { 1 } x ^ { 11 } d x$

Evaluate $\int \frac { x ^ { 5 } } { x ^ { 6 } + 3 } d x$ .

Evaluate $\int \left( 1 - \frac { 9 } { x } + \frac { 5 } { x ^ { 7 } } \right) d x$ .

Evaluate $\int \left( e ^ { 2 t } + e ^ { - 3 t } \right) d t$ .

Evaluate $\int x ^ { 6 } \sqrt { x ^ { 7 } + 4 } d x$

Functions, Graphs, and Limits

Differentiation: Basic Concepts

Additional Applications of the Derivative

Exponential and Logarithmic Functions

Additional Topics in Integration

Calculus of Several Variables

Appendix: Algebra Review

Filters

Exam 5: Integration

For the demand function D(q)=400(0.2q+1)2D ( q ) = \frac { 400 } { ( 0.2 q + 1 ) ^ { 2 } }D(q)=(0.2q+1)2400​ dollars per unit, find the total amount of money consumer's are willing to spend when q = 3 units.

∫2xx2−2dx=2(x2−2)3/23+C\int 2 x \sqrt { x ^ { 2 } - 2 } d x = \frac { 2 \left( x ^ { 2 } - 2 \right) ^ { 3 / 2 } } { 3 } + C∫2xx2−2​dx=32(x2−2)3/2​+C

Given an initial population, P0=60,000P _ { 0 } = 60,000P0​=60,000 , a renewal rate, R = 189, and a survival function, S(t)=e−0.05tS ( t ) = e ^ { - 0.05 t }S(t)=e−0.05t , with time t measured in years, determine the population at the end of 11 years.

Evaluate ∫(x3−3x2+5)dx\int \left( x ^ { 3 } - 3 x ^ { 2 } + 5 \right) d x∫(x3−3x2+5)dx .

Evaluate ∫−11x11dx\int _ { - 1 } ^ { 1 } x ^ { 11 } d x∫−11​x11dx .

Evaluate ∫(1−3x+5x3)dx\int \left( 1 - \frac { 3 } { x } + \frac { 5 } { x ^ { 3 } } \right) d x∫(1−x3​+x35​)dx .

Evaluate ∫e9x−6dx\int e ^ { 9 x - 6 } d x∫e9x−6dx .

The slope f′(x)f ^ { \prime } ( x )f′(x) at each point (x, y) on a curve y = f (x) is given, along with a particular point (a,b) on the curve. Use this information to find f (x).

Evaluate ∫233x−2x5dx\int _ { 2 } ^ { 3 } \frac { 3 x - 2 } { x ^ { 5 } } d x∫23​x53x−2​dx . Approximate to four decimal places.

Evaluate ∫(4x7−ex)dx\int \left( 4 x ^ { 7 } - e ^ { x } \right) d x∫(4x7−ex)dx .

Compute the area of the finite region bounded by the graphs of the functions y=5x2y = 5 x ^ { 2 }y=5x2 , and y=−5x2−20x+80y = - 5 x ^ { 2 } - 20 x + 80y=−5x2−20x+80

Find the average value of f (x) = 2x + 3 over the interval 0 ≤\le≤ x ≤\le≤ 5.

Evaluate ∫−1152x+33dx\int _ { - 1 } ^ { 1 } \frac { 5 } { \sqrt [ 3 ] { 2 x + 3 } } d x∫−11​32x+3​5​dx . Approximate your answer to two decimal places, if necessary.

Find the volume of the solid of revolution formed by rotating the region R about the x-axis.R is the region under the curve y=4−x2y = \sqrt { 4 - x ^ { 2 } }y=4−x2​ from x = -2 to x = 2.

Evaluate ∫−11x11dx\int _ { - 1 } ^ { 1 } x ^ { 11 } d x∫−11​x11dx

Evaluate ∫x5x6+3dx\int \frac { x ^ { 5 } } { x ^ { 6 } + 3 } d x∫x6+3x5​dx .

Evaluate ∫(1−9x+5x7)dx\int \left( 1 - \frac { 9 } { x } + \frac { 5 } { x ^ { 7 } } \right) d x∫(1−x9​+x75​)dx .

Evaluate ∫(e2t+e−3t)dt\int \left( e ^ { 2 t } + e ^ { - 3 t } \right) d t∫(e2t+e−3t)dt .

Evaluate ∫x6x7+4dx\int x ^ { 6 } \sqrt { x ^ { 7 } + 4 } d x∫x6x7+4​dx

Functions, Graphs, and Limits

Differentiation: Basic Concepts

Additional Applications of the Derivative

Exponential and Logarithmic Functions

Additional Topics in Integration

Calculus of Several Variables

Appendix: Algebra Review

Filters

For the demand function $D ( q ) = \frac { 400 } { ( 0.2 q + 1 ) ^ { 2 } }$ dollars per unit, find the total amount of money consumer's are willing to spend when q = 3 units.

$\int 2 x \sqrt { x ^ { 2 } - 2 } d x = \frac { 2 \left( x ^ { 2 } - 2 \right) ^ { 3 / 2 } } { 3 } + C$

Given an initial population, $P _ { 0 } = 60,000$ , a renewal rate, R = 189, and a survival function, $S ( t ) = e ^ { - 0.05 t }$ , with time t measured in years, determine the population at the end of 11 years.

Evaluate $\int \left( x ^ { 3 } - 3 x ^ { 2 } + 5 \right) d x$ .

Evaluate $\int _ { - 1 } ^ { 1 } x ^ { 11 } d x$ .

Evaluate $\int \left( 1 - \frac { 3 } { x } + \frac { 5 } { x ^ { 3 } } \right) d x$ .

Evaluate $\int e ^ { 9 x - 6 } d x$ .

The slope $f ^ { \prime } ( x )$ at each point (x, y) on a curve y = f (x) is given, along with a particular point (a,b) on the curve. Use this information to find f (x).

Evaluate $\int _ { 2 } ^ { 3 } \frac { 3 x - 2 } { x ^ { 5 } } d x$ . Approximate to four decimal places.

Evaluate $\int \left( 4 x ^ { 7 } - e ^ { x } \right) d x$ .

Compute the area of the finite region bounded by the graphs of the functions $y = 5 x ^ { 2 }$ , and $y = - 5 x ^ { 2 } - 20 x + 80$

Find the average value of f (x) = 2x + 3 over the interval 0 $\le$ x $\le$ 5.

Evaluate $\int _ { - 1 } ^ { 1 } \frac { 5 } { \sqrt [ 3 ] { 2 x + 3 } } d x$ . Approximate your answer to two decimal places, if necessary.

Find the volume of the solid of revolution formed by rotating the region R about the x-axis.R is the region under the curve $y = \sqrt { 4 - x ^ { 2 } }$ from x = -2 to x = 2.

Evaluate $\int _ { - 1 } ^ { 1 } x ^ { 11 } d x$

Evaluate $\int \frac { x ^ { 5 } } { x ^ { 6 } + 3 } d x$ .

Evaluate $\int \left( 1 - \frac { 9 } { x } + \frac { 5 } { x ^ { 7 } } \right) d x$ .

Evaluate $\int \left( e ^ { 2 t } + e ^ { - 3 t } \right) d t$ .

Evaluate $\int x ^ { 6 } \sqrt { x ^ { 7 } + 4 } d x$