Question 1

Evaluate $\int 5 x ^ { 4 } e ^ { x ^ { 5 } } d x$ .

Accepted Answer

A)  $e ^ {{ x } ^{6}}+ C$ 
B)  $e ^ { x ^ { 5 } } + C$ 
C)  $x ^ { 5 } e ^ { x ^ { 5 } } + C$ 
D)  $25 x ^ { 5 } e ^ { x ^ { 5 } } + C$ 
A)  $e ^ {{ x } ^{6}}+ C$ 
B)  $e ^ { x ^ { 5 } } + C$ 
C)  $x ^ { 5 } e ^ { x ^ { 5 } } + C$ 
D)  $25 x ^ { 5 } e ^ { x ^ { 5 } } + C$

Question 2

Evaluate the indicated integral: $$\int \frac { 7 x ^ { 4 } + 56 x ^ { 3 } + 56 } { x ^ { 5 } + 10 x ^ { 4 } + 40 x + 4 } d x$$

Accepted Answer

A)  $\frac { 7 } { 5 } \ln \left| x ^ { 5 } + 10 x ^ { 4 } + 40 x + 4 \right| + C$ 
B)  $\frac { 5 } { 7 } \ln \left| x ^ { 5 } + 10 x ^ { 4 } + 40 x + 4 \right| + C$ 
C)  $\frac { 7 } { 5 } \ln \left| x ^ { 4 } + 8 x ^ { 3 } + 8 \right| + C$ 
D)  $\frac { 7 } { 5 } \ln \left| x ^ { 5 } + 10 x ^ { 4 } + 32 x \right| + C$ 
A)  $\frac { 7 } { 5 } \ln \left| x ^ { 5 } + 10 x ^ { 4 } + 40 x + 4 \right| + C$ 
B)  $\frac { 5 } { 7 } \ln \left| x ^ { 5 } + 10 x ^ { 4 } + 40 x + 4 \right| + C$ 
C)  $\frac { 7 } { 5 } \ln \left| x ^ { 4 } + 8 x ^ { 3 } + 8 \right| + C$ 
D)  $\frac { 7 } { 5 } \ln \left| x ^ { 5 } + 10 x ^ { 4 } + 32 x \right| + C$

Question 3

Records indicate that t hours past midnight, the temperature at the local airport was $f ( t ) = - 0.3 t ^ { 2 } + 6 t + 12$ degrees Fahrenheit. What was the average temperature at the airport between 5:00 A.M. and noon? Round your answer to one decimal place, if necessary.

Accepted Answer

A)  75.1 degrees F 
B)  40.1 degrees F 
C)  28.1 degrees F 
D)  16.5 degrees F 
A)  75.1 degrees F 
B)  40.1 degrees F 
C)  28.1 degrees F 
D)  16.5 degrees F

Question 4

Evaluate $\int 9 x ^ { 8 } e ^ { x ^ { 9 } } d x$ .

Accepted Answer

A)  $e ^ { x ^ { 9 } } + C$ 
B)  $e ^ { x ^ { 10 } } + C$ 
C)  $x ^ { 9 } e ^ { x ^ { 9 } } + C$ 
D)  $81 x ^ { 9 } e ^ { x ^ { 9 } } + C$ 
A)  $e ^ { x ^ { 9 } } + C$ 
B)  $e ^ { x ^ { 10 } } + C$ 
C)  $x ^ { 9 } e ^ { x ^ { 9 } } + C$ 
D)  $81 x ^ { 9 } e ^ { x ^ { 9 } } + C$

Question 5

An object is moving along a straight line in such a way that after t minutes, its speed is $v ( t ) = 4 t ^ { 2 } + 3 t + 1$ meters per minute. How far does the object travel during the 3rd minute?

Accepted Answer

A)  $\frac { 203 } { 6 }$ meters 
B)  $\frac { 205 } { 6 }$ meters 
C)  $\frac { 209 } { 6 }$ meters 
D)  $\frac { 211 } { 6 }$ meters 
A)  $\frac { 203 } { 6 }$ meters 
B)  $\frac { 205 } { 6 }$ meters 
C)  $\frac { 209 } { 6 }$ meters 
D)  $\frac { 211 } { 6 }$ meters

Question 6

$\int \left( \frac { 5 } { x ^ { 2 } } - \frac { 2 } { x ^ { 3 } } + \frac { 5 } { \sqrt { x } } \right) d x = - \frac { 5 } { x } + \frac { 1 } { x ^ { 2 } } + 5 \ln | \sqrt { x } | + C$

Accepted Answer

A) True 
 B)False

Question 7

Evaluate $\int _ { 1 } ^ { 2 } \left( 3 - \frac { 8 } { x } + \frac { 3 } { x ^ { 3 } } \right) d x$ .

Accepted Answer

The answer of Evaluate \(\int _ { 1 } ^...

Question 8

Evaluate $\int \frac { x } { \sqrt { x ^ { 2 } + 6 } } d x$ .

Accepted Answer

The answer of Evaluate \(\int \frac { x } {...

Question 9

Evaluate $\int x ^ { 2 } \left( x ^ { 3 } + 9 \right) ^ { 1 / 2 } d x$ .

Accepted Answer

A)  $\frac { 2 } { 9 } \left( x ^ { 3 } + 9 \right) ^ { 3 / 2 } + C$ 
B)  $\left( x ^ { 3 } + 9 \right) ^ { 3 / 2 } + C$ 
C)  $C \left( x ^ { 3 } + 9 \right) ^ { 3 / 2 }$ 
D)  $x ^ { 3 } + 9 + C$ 
A)  $\frac { 2 } { 9 } \left( x ^ { 3 } + 9 \right) ^ { 3 / 2 } + C$ 
B)  $\left( x ^ { 3 } + 9 \right) ^ { 3 / 2 } + C$ 
C)  $C \left( x ^ { 3 } + 9 \right) ^ { 3 / 2 }$ 
D)  $x ^ { 3 } + 9 + C$

Question 10

$\int ( x - 7 ) ^ { 8 } d x = \frac { ( x - 7 ) ^ { 9 } } { 9 } + C$

Accepted Answer

A) True 
 B)False

Question 11

A certain nuclear power plant produces nuclear waste in the form of strontium-90 at the constant rate of 400 pounds per year. The waste decays exponentially with a half-life of 28 years. How much of the radioactive waste from the nuclear plant will be present after 80 years? [Hint: Think of this as a survival and renewal problem.] Round to two decimal places.

Accepted Answer

The answer of A certain nuclear power plant produces nuclear...

Question 12

Evaluate $\int \left( e ^ { - 8 x } + \frac { 8 } { x } \right) d x$ .

Accepted Answer

The answer of Evaluate \(\int \left( e ^ { -...

Question 13

In a certain section of the country, the price of chicken is currently $2 per kilogram. It is estimated that x weeks from now, the price will be increasing at a rate of $2 \sqrt { x + 1 }$ cents per kilogram. How much will chicken cost 5 weeks from now?

Accepted Answer

A)  $2.18 per kilogram 
B)  $0.19 per kilogram 
C)  $3.18 per kilogram 
D)  $1.19 per kilogram 
A)  $2.18 per kilogram 
B)  $0.19 per kilogram 
C)  $3.18 per kilogram 
D)  $1.19 per kilogram

Question 14

Evaluate $\int \left( \frac { x } { 7 } - 2 \right) ^ { 2 / 7 } d x$ .

Accepted Answer

A)  $\frac { 49 } { 9 } \left( \frac { x } { 7 } - 2 \right) ^ { 9 / 7 } + C$ 
B)  $\frac { x ^ { 2 } } { 14 } - 2 x + C$ 
C)  $\frac { 7 } { 9 } \left( \frac { x } { 7 } - 2 \right) ^ { 9 / 7 } + C$ 
D)  $\left( \frac { x } { 7 } - 2 \right) ^ { 9 / 7 } + C$ 
A)  $\frac { 49 } { 9 } \left( \frac { x } { 7 } - 2 \right) ^ { 9 / 7 } + C$ 
B)  $\frac { x ^ { 2 } } { 14 } - 2 x + C$ 
C)  $\frac { 7 } { 9 } \left( \frac { x } { 7 } - 2 \right) ^ { 9 / 7 } + C$ 
D)  $\left( \frac { x } { 7 } - 2 \right) ^ { 9 / 7 } + C$

Question 15

Evaluate $\int 5 x ^ { 4 } e ^ { x ^ { 5 } } d x$

Accepted Answer

A)  $e ^ {{ x } ^6}+ C$ 
B)  $x ^ { 5 } e ^ { x ^ { 5 } } + C$ 
C)  $2.5 x ^ { 5 } e ^ { x ^ { 5 } } + C$ 
D)  $e ^ { x ^ { 5 } } + C$ 
A)  $e ^ {{ x } ^6}+ C$ 
B)  $x ^ { 5 } e ^ { x ^ { 5 } } + C$ 
C)  $2.5 x ^ { 5 } e ^ { x ^ { 5 } } + C$ 
D)  $e ^ { x ^ { 5 } } + C$

Question 16

Evaluate $\int \frac { x d x } { \sqrt { x ^ { 2 } + 1 } }$ .

Accepted Answer

The answer of Evaluate \(\int \frac { x d x...

Question 17

Evaluate $\int \left( 5 x ^ { 2 / 3 } - \frac { 3 } { x ^ { 5 } } + \frac { 1 } { 3 x } \right) d x$ .

Accepted Answer

The answer of Evaluate \(\int \left( 5 x ^ {...

Question 18

Determine the area of the region bounded by the curves $y = e ^ { x }$ and $y = e ^ { - x }$ between x = 0 and x = ln 6.

Accepted Answer

The answer of Determine the area of the region bounded...

Question 19

Money is transferred continuously into an account at the constant rate of $900 per year. The account earns interest at the annual rate of 5% compounded continuously. How much will be in the account at the end of 4 years?

Accepted Answer

A)  $2,197.52 
B)  $133,002.01 
C)  $3,985.25 
D)  $3,600.00 
A)  $2,197.52 
B)  $133,002.01 
C)  $3,985.25 
D)  $3,600.00

Question 20

Evaluate $\int \left( \frac { x } { 9 } - 9 \right) ^ { 2 / 9 } d x$

Accepted Answer

A)  $\left( \frac { x } { 9 } - 9 \right) ^ { 11 / 9 } + C$ 
B)  $\frac { 9 } { 11 } \left( \frac { x } { 9 } - 9 \right) ^ { 11 / 9 } + C$ 
C)  $\frac { 81 } { 11 } \left( \frac { x } { 9 } - 9 \right) ^ { 11 / 9 } + C$ 
D)  $\frac { x ^ { 2 } } { 18 } - 9 x + C$ 
A)  $\left( \frac { x } { 9 } - 9 \right) ^ { 11 / 9 } + C$ 
B)  $\frac { 9 } { 11 } \left( \frac { x } { 9 } - 9 \right) ^ { 11 / 9 } + C$ 
C)  $\frac { 81 } { 11 } \left( \frac { x } { 9 } - 9 \right) ^ { 11 / 9 } + C$ 
D)  $\frac { x ^ { 2 } } { 18 } - 9 x + C$

Evaluate $\int 5 x ^ { 4 } e ^ { x ^ { 5 } } d x$ .

Evaluate the indicated integral: $\int \frac { 7 x ^ { 4 } + 56 x ^ { 3 } + 56 } { x ^ { 5 } + 10 x ^ { 4 } + 40 x + 4 } d x$

Records indicate that t hours past midnight, the temperature at the local airport was $f ( t ) = - 0.3 t ^ { 2 } + 6 t + 12$ degrees Fahrenheit. What was the average temperature at the airport between 5:00 A.M. and noon? Round your answer to one decimal place, if necessary.

Evaluate $\int 9 x ^ { 8 } e ^ { x ^ { 9 } } d x$ .

An object is moving along a straight line in such a way that after t minutes, its speed is $v ( t ) = 4 t ^ { 2 } + 3 t + 1$ meters per minute. How far does the object travel during the 3rd minute?

$\int \left( \frac { 5 } { x ^ { 2 } } - \frac { 2 } { x ^ { 3 } } + \frac { 5 } { \sqrt { x } } \right) d x = - \frac { 5 } { x } + \frac { 1 } { x ^ { 2 } } + 5 \ln | \sqrt { x } | + C$

Evaluate $\int _ { 1 } ^ { 2 } \left( 3 - \frac { 8 } { x } + \frac { 3 } { x ^ { 3 } } \right) d x$ .

Evaluate $\int \frac { x } { \sqrt { x ^ { 2 } + 6 } } d x$ .

Evaluate $\int x ^ { 2 } \left( x ^ { 3 } + 9 \right) ^ { 1 / 2 } d x$ .

$\int ( x - 7 ) ^ { 8 } d x = \frac { ( x - 7 ) ^ { 9 } } { 9 } + C$

Evaluate $\int \left( e ^ { - 8 x } + \frac { 8 } { x } \right) d x$ .

In a certain section of the country, the price of chicken is currently $2 per kilogram. It is estimated that x weeks from now, the price will be increasing at a rate of $2 \sqrt { x + 1 }$ cents per kilogram. How much will chicken cost 5 weeks from now?

Evaluate $\int \left( \frac { x } { 7 } - 2 \right) ^ { 2 / 7 } d x$ .

Evaluate $\int 5 x ^ { 4 } e ^ { x ^ { 5 } } d x$

Evaluate $\int \frac { x d x } { \sqrt { x ^ { 2 } + 1 } }$ .

Evaluate $\int \left( 5 x ^ { 2 / 3 } - \frac { 3 } { x ^ { 5 } } + \frac { 1 } { 3 x } \right) d x$ .

Determine the area of the region bounded by the curves $y = e ^ { x }$ and $y = e ^ { - x }$ between x = 0 and x = ln 6.

Money is transferred continuously into an account at the constant rate of $900 per year. The account earns interest at the annual rate of 5% compounded continuously. How much will be in the account at the end of 4 years?

Evaluate $\int \left( \frac { x } { 9 } - 9 \right) ^ { 2 / 9 } d x$

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

Evaluate ∫5x4ex5dx\int 5 x ^ { 4 } e ^ { x ^ { 5 } } d x∫5x4ex5dx .

Evaluate the indicated integral: ∫7x4+56x3+56x5+10x4+40x+4dx\int \frac { 7 x ^ { 4 } + 56 x ^ { 3 } + 56 } { x ^ { 5 } + 10 x ^ { 4 } + 40 x + 4 } d x∫x5+10x4+40x+47x4+56x3+56​dx

Evaluate ∫9x8ex9dx\int 9 x ^ { 8 } e ^ { x ^ { 9 } } d x∫9x8ex9dx .

An object is moving along a straight line in such a way that after t minutes, its speed is v(t)=4t2+3t+1v ( t ) = 4 t ^ { 2 } + 3 t + 1v(t)=4t2+3t+1 meters per minute. How far does the object travel during the 3rd minute?

∫(5x2−2x3+5x)dx=−5x+1x2+5ln⁡∣x∣+C\int \left( \frac { 5 } { x ^ { 2 } } - \frac { 2 } { x ^ { 3 } } + \frac { 5 } { \sqrt { x } } \right) d x = - \frac { 5 } { x } + \frac { 1 } { x ^ { 2 } } + 5 \ln | \sqrt { x } | + C∫(x25​−x32​+x​5​)dx=−x5​+x21​+5ln∣x​∣+C

Evaluate ∫12(3−8x+3x3)dx\int _ { 1 } ^ { 2 } \left( 3 - \frac { 8 } { x } + \frac { 3 } { x ^ { 3 } } \right) d x∫12​(3−x8​+x33​)dx .

Evaluate ∫xx2+6dx\int \frac { x } { \sqrt { x ^ { 2 } + 6 } } d x∫x2+6​x​dx .

Evaluate ∫x2(x3+9)1/2dx\int x ^ { 2 } \left( x ^ { 3 } + 9 \right) ^ { 1 / 2 } d x∫x2(x3+9)1/2dx .

∫(x−7)8dx=(x−7)99+C\int ( x - 7 ) ^ { 8 } d x = \frac { ( x - 7 ) ^ { 9 } } { 9 } + C∫(x−7)8dx=9(x−7)9​+C

Evaluate ∫(e−8x+8x)dx\int \left( e ^ { - 8 x } + \frac { 8 } { x } \right) d x∫(e−8x+x8​)dx .

In a certain section of the country, the price of chicken is currently $2 per kilogram. It is estimated that x weeks from now, the price will be increasing at a rate of 2x+12 \sqrt { x + 1 }2x+1​ cents per kilogram. How much will chicken cost 5 weeks from now?

Evaluate ∫(x7−2)2/7dx\int \left( \frac { x } { 7 } - 2 \right) ^ { 2 / 7 } d x∫(7x​−2)2/7dx .

Evaluate ∫5x4ex5dx\int 5 x ^ { 4 } e ^ { x ^ { 5 } } d x∫5x4ex5dx

Evaluate ∫xdxx2+1\int \frac { x d x } { \sqrt { x ^ { 2 } + 1 } }∫x2+1​xdx​ .

Evaluate ∫(5x2/3−3x5+13x)dx\int \left( 5 x ^ { 2 / 3 } - \frac { 3 } { x ^ { 5 } } + \frac { 1 } { 3 x } \right) d x∫(5x2/3−x53​+3x1​)dx .

Determine the area of the region bounded by the curves y=exy = e ^ { x }y=ex and y=e−xy = e ^ { - x }y=e−x between x = 0 and x = ln 6.

Money is transferred continuously into an account at the constant rate of $900 per year. The account earns interest at the annual rate of 5% compounded continuously. How much will be in the account at the end of 4 years?

Evaluate ∫(x9−9)2/9dx\int \left( \frac { x } { 9 } - 9 \right) ^ { 2 / 9 } d x∫(9x​−9)2/9dx

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

Evaluate $\int 5 x ^ { 4 } e ^ { x ^ { 5 } } d x$ .

Evaluate the indicated integral: $\int \frac { 7 x ^ { 4 } + 56 x ^ { 3 } + 56 } { x ^ { 5 } + 10 x ^ { 4 } + 40 x + 4 } d x$

Evaluate $\int 9 x ^ { 8 } e ^ { x ^ { 9 } } d x$ .

An object is moving along a straight line in such a way that after t minutes, its speed is $v ( t ) = 4 t ^ { 2 } + 3 t + 1$ meters per minute. How far does the object travel during the 3rd minute?

$\int \left( \frac { 5 } { x ^ { 2 } } - \frac { 2 } { x ^ { 3 } } + \frac { 5 } { \sqrt { x } } \right) d x = - \frac { 5 } { x } + \frac { 1 } { x ^ { 2 } } + 5 \ln | \sqrt { x } | + C$

Evaluate $\int _ { 1 } ^ { 2 } \left( 3 - \frac { 8 } { x } + \frac { 3 } { x ^ { 3 } } \right) d x$ .

Evaluate $\int \frac { x } { \sqrt { x ^ { 2 } + 6 } } d x$ .

Evaluate $\int x ^ { 2 } \left( x ^ { 3 } + 9 \right) ^ { 1 / 2 } d x$ .

$\int ( x - 7 ) ^ { 8 } d x = \frac { ( x - 7 ) ^ { 9 } } { 9 } + C$

Evaluate $\int \left( e ^ { - 8 x } + \frac { 8 } { x } \right) d x$ .

In a certain section of the country, the price of chicken is currently $2 per kilogram. It is estimated that x weeks from now, the price will be increasing at a rate of $2 \sqrt { x + 1 }$ cents per kilogram. How much will chicken cost 5 weeks from now?

Evaluate $\int \left( \frac { x } { 7 } - 2 \right) ^ { 2 / 7 } d x$ .

Evaluate $\int 5 x ^ { 4 } e ^ { x ^ { 5 } } d x$

Evaluate $\int \frac { x d x } { \sqrt { x ^ { 2 } + 1 } }$ .

Evaluate $\int \left( 5 x ^ { 2 / 3 } - \frac { 3 } { x ^ { 5 } } + \frac { 1 } { 3 x } \right) d x$ .

Determine the area of the region bounded by the curves $y = e ^ { x }$ and $y = e ^ { - x }$ between x = 0 and x = ln 6.

Evaluate $\int \left( \frac { x } { 9 } - 9 \right) ^ { 2 / 9 } d x$