Question 1

Evaluate $\int \left( 5 x ^ { 3 } - 3 x + 4 \right) d x$ .

Accepted Answer

A)  $\frac { 5 x ^ { 4 } } { 4 } - \frac { 3 x ^ { 2 } } { 2 } + 4 x + C$ 
B)  $15 x ^ { 2 } - 3 + C$ 
C)  $5 x ^ { 4 } - 3 x ^ { 2 } + 4 x + C$ 
D)  $\frac { 5 x ^ { 4 } } { 4 } - \frac { 3 x ^ { 2 } } { 2 } + C$ 
A)  $\frac { 5 x ^ { 4 } } { 4 } - \frac { 3 x ^ { 2 } } { 2 } + 4 x + C$ 
B)  $15 x ^ { 2 } - 3 + C$ 
C)  $5 x ^ { 4 } - 3 x ^ { 2 } + 4 x + C$ 
D)  $\frac { 5 x ^ { 4 } } { 4 } - \frac { 3 x ^ { 2 } } { 2 } + C$

Question 2

Solve the given initial value problem for y = f (x). $$\frac { d y } { d x } = \frac { x + 5 } { x ^ { 2 } + 10 x + 3 }$$ where y = 6 when x = 1

Accepted Answer

A)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right| - \frac { 1 } { 2 } \ln 14 + 6$ 
B)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right| - \frac { 1 } { 2 } \ln 14$ 
C)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right| + 6$ 
D)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right|$ 
A)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right| - \frac { 1 } { 2 } \ln 14 + 6$ 
B)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right| - \frac { 1 } { 2 } \ln 14$ 
C)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right| + 6$ 
D)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right|$

Question 3

Evaluate $\int \frac { 4 x - 1 } { x ^ { 5 } } d x$ .

Accepted Answer

The answer of Evaluate \(\int \frac { 4 x -...

Question 4

Evaluate $\int _ { - 2 } ^ { 2 } \left( x ^ { 5 } + 3 x ^ { 3 } - 2 x \right) d x$ . Round answer to three decimal places, if necessary.

Accepted Answer

A)  50.123 
B)  4 
C)  0 
D)  6.892 
A)  50.123 
B)  4 
C)  0 
D)  6.892

Question 5

A television program currently has P0 = 14 million loyal watchers, and new people are expected to begin watching at the rate of $R ( t ) = 0.4 e ^ { 0.01 t }$ per year. The fraction of people still watching after t years is expected to be $S ( t ) = e ^ { - 0.025 t }$ . How many watchers will there be after 4 years? Round to one decimal place.

Accepted Answer

Question 6

$\int _ { 0 } ^ { 8 } \left( \sqrt [ 3 ] { t ^ { 2 } } + \frac { 1 } { \sqrt { t + 1 } } \right) d t = \frac { 116 } { 5 }$

Accepted Answer

A) True 
 B)False

Question 7

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 $y = \frac { 1 } { x ^ { 2 } }$ from x = 1 to x = 4.

Accepted Answer

The answer of Find the volume of the solid of...

Evaluate $\int \left( 5 x ^ { 3 } - 3 x + 4 \right) d x$ .

Solve the given initial value problem for y = f (x). $\frac { d y } { d x } = \frac { x + 5 } { x ^ { 2 } + 10 x + 3 }$ where y = 6 when x = 1

Evaluate $\int \frac { 4 x - 1 } { x ^ { 5 } } d x$ .

Evaluate $\int _ { - 2 } ^ { 2 } \left( x ^ { 5 } + 3 x ^ { 3 } - 2 x \right) d x$ . Round answer to three decimal places, if necessary.

$\int _ { 0 } ^ { 8 } \left( \sqrt [ 3 ] { t ^ { 2 } } + \frac { 1 } { \sqrt { t + 1 } } \right) d t = \frac { 116 } { 5 }$

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 $y = \frac { 1 } { x ^ { 2 } }$ from x = 1 to x = 4.

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 ∫(5x3−3x+4)dx\int \left( 5 x ^ { 3 } - 3 x + 4 \right) d x∫(5x3−3x+4)dx .

Solve the given initial value problem for y = f (x). dydx=x+5x2+10x+3\frac { d y } { d x } = \frac { x + 5 } { x ^ { 2 } + 10 x + 3 }dxdy​=x2+10x+3x+5​ where y = 6 when x = 1

Evaluate ∫4x−1x5dx\int \frac { 4 x - 1 } { x ^ { 5 } } d x∫x54x−1​dx .

Evaluate ∫−22(x5+3x3−2x)dx\int _ { - 2 } ^ { 2 } \left( x ^ { 5 } + 3 x ^ { 3 } - 2 x \right) d x∫−22​(x5+3x3−2x)dx . Round answer to three decimal places, if necessary.

∫08(t23+1t+1)dt=1165\int _ { 0 } ^ { 8 } \left( \sqrt [ 3 ] { t ^ { 2 } } + \frac { 1 } { \sqrt { t + 1 } } \right) d t = \frac { 116 } { 5 }∫08​(3t2​+t+1​1​)dt=5116​

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=1x2y = \frac { 1 } { x ^ { 2 } }y=x21​ from x = 1 to x = 4.

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 $\int \left( 5 x ^ { 3 } - 3 x + 4 \right) d x$ .

Solve the given initial value problem for y = f (x). $\frac { d y } { d x } = \frac { x + 5 } { x ^ { 2 } + 10 x + 3 }$ where y = 6 when x = 1

Evaluate $\int \frac { 4 x - 1 } { x ^ { 5 } } d x$ .

Evaluate $\int _ { - 2 } ^ { 2 } \left( x ^ { 5 } + 3 x ^ { 3 } - 2 x \right) d x$ . Round answer to three decimal places, if necessary.

$\int _ { 0 } ^ { 8 } \left( \sqrt [ 3 ] { t ^ { 2 } } + \frac { 1 } { \sqrt { t + 1 } } \right) d t = \frac { 116 } { 5 }$

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 $y = \frac { 1 } { x ^ { 2 } }$ from x = 1 to x = 4.