Question 1

The integral $\int \frac { 1 } { ( x + 2 ) \left( x ^ { 2 } + 1 \right) } d x$ is

Accepted Answer

A)  $\frac { 2 \ln | x + 2 | + 4 \tan ^ { - 1 } ( x ) - \ln \left| x ^ { 2 } + 1 \right| } { 10 } + C$ 
B)  $\frac { 2 \ln | x + 2 | - 4 \tan ^ { - 1 } ( x ) - \ln \left| x ^ { 2 } + 1 \right| } { 10 } + C$ 
C)  $\frac { 2 \ln | x + 2 | + 4 \tan ^ { - 1 } ( x ) + \ln \left| x ^ { 2 } + 1 \right| } { 10 } + C$ 
D)  $- \frac { 2 \ln | x + 2 | + 4 \tan ^ { - 1 } ( x ) - \ln \left| x ^ { 2 } + 1 \right| } { 10 } + C$ 
E)  $- \frac { 2 \ln | x + 2 | - 4 \tan ^ { - 1 } ( x ) + \ln \left| x ^ { 2 } + 1 \right| } { 10 } + C$ 
A)  $\frac { 2 \ln | x + 2 | + 4 \tan ^ { - 1 } ( x ) - \ln \left| x ^ { 2 } + 1 \right| } { 10 } + C$ 
B)  $\frac { 2 \ln | x + 2 | - 4 \tan ^ { - 1 } ( x ) - \ln \left| x ^ { 2 } + 1 \right| } { 10 } + C$ 
C)  $\frac { 2 \ln | x + 2 | + 4 \tan ^ { - 1 } ( x ) + \ln \left| x ^ { 2 } + 1 \right| } { 10 } + C$ 
D)  $- \frac { 2 \ln | x + 2 | + 4 \tan ^ { - 1 } ( x ) - \ln \left| x ^ { 2 } + 1 \right| } { 10 } + C$ 
E)  $- \frac { 2 \ln | x + 2 | - 4 \tan ^ { - 1 } ( x ) + \ln \left| x ^ { 2 } + 1 \right| } { 10 } + C$

Question 2

The integral $\int \frac { 1 } { x ^ { 2 } + 2 x - 15 } d x$ is

Accepted Answer

A)  $\tan ^ { - 1 } ( x - 3 ) + C$ 
B)  $\frac { \ln \left| \frac { x - 3 } { x + 5 } \right| } { 8 } + C$ 
C)  $\ln \left( x ^ { 2 } + 2 x - 15 \right) + C$ 
D)  $\frac { x \sqrt { x ^ { 2 } + 4 } - 4 \sinh ^ { - 1 } \left( \frac { x } { 2 } \right) } { 2 } + C$ 
E)  $6 \sin ^ { - 1 } ( x - 3 ) + \sqrt { x ^ { 2 } - 6 x + 10 } + C$ 
A)  $\tan ^ { - 1 } ( x - 3 ) + C$ 
B)  $\frac { \ln \left| \frac { x - 3 } { x + 5 } \right| } { 8 } + C$ 
C)  $\ln \left( x ^ { 2 } + 2 x - 15 \right) + C$ 
D)  $\frac { x \sqrt { x ^ { 2 } + 4 } - 4 \sinh ^ { - 1 } \left( \frac { x } { 2 } \right) } { 2 } + C$ 
E)  $6 \sin ^ { - 1 } ( x - 3 ) + \sqrt { x ^ { 2 } - 6 x + 10 } + C$

Question 3

The integral $\int \frac { 1 } { 4 x ^ { 2 } - 12 x + 5 } d x$ is

Accepted Answer

A)  $- \frac { \ln \left| \frac { 2 x - 5 } { 2 x - 1 } \right| } { 4 } + C$ 
B)  $\frac { \ln \left| \frac { x - 3 } { x + 5 } \right| } { 4 } + C$ 
C)  $- \frac { \ln \left| \frac { 2 x - 5 } { 2 x - 1 } \right| } { 8 } + C$ 
D)  $\frac { \ln \left| \frac { 2 x - 5 } { 2 x - 1 } \right| } { 8 } + C$ 
E)  $\frac { \ln \left| \frac { 2 x - 5 } { 2 x - 1 } \right| } { 2 } + C$ 
A)  $- \frac { \ln \left| \frac { 2 x - 5 } { 2 x - 1 } \right| } { 4 } + C$ 
B)  $\frac { \ln \left| \frac { x - 3 } { x + 5 } \right| } { 4 } + C$ 
C)  $- \frac { \ln \left| \frac { 2 x - 5 } { 2 x - 1 } \right| } { 8 } + C$ 
D)  $\frac { \ln \left| \frac { 2 x - 5 } { 2 x - 1 } \right| } { 8 } + C$ 
E)  $\frac { \ln \left| \frac { 2 x - 5 } { 2 x - 1 } \right| } { 2 } + C$

Question 4

The integral $\int \cos ^ { - 1 } x d x$ is

Accepted Answer

A)  $x \cos ^ { - 1 } x - \sqrt { x ^ { 2 } - 1 } + C$ 
B)  $x \cos ^ { - 1 } x + \sqrt { x ^ { 2 } - 1 } + C$ 
C)  $- x \cos ^ { - 1 } x + \sqrt { 1 - x ^ { 2 } } + C$ 
D)  $x \cos ^ { - 1 } x + \sqrt { 1 - x ^ { 2 } } + C$ 
E)  $x \cos ^ { - 1 } x - \sqrt { 1 - x ^ { 2 } } + C$ 
A)  $x \cos ^ { - 1 } x - \sqrt { x ^ { 2 } - 1 } + C$ 
B)  $x \cos ^ { - 1 } x + \sqrt { x ^ { 2 } - 1 } + C$ 
C)  $- x \cos ^ { - 1 } x + \sqrt { 1 - x ^ { 2 } } + C$ 
D)  $x \cos ^ { - 1 } x + \sqrt { 1 - x ^ { 2 } } + C$ 
E)  $x \cos ^ { - 1 } x - \sqrt { 1 - x ^ { 2 } } + C$

Question 5

Using Simpson's Rule with n = 4, the approximated value of $\int _ { 0 } ^ { 2 } \frac { 1 } { x + 1 } d x,$ to three decimal places, is

Accepted Answer

A)  $0.997$ 
B)  $1.099$ 
C)  $1.209$ 
D)  $1.231$ 
E)  $1.367$ 
A)  $0.997$ 
B)  $1.099$ 
C)  $1.209$ 
D)  $1.231$ 
E)  $1.367$

Question 6

Using Simpson's Rule with n = 4, the approximated value of $\int _ { 1 } ^ { 2 } \frac { e ^ { x } } { x } d x,$ to three decimal places, is

Accepted Answer

A)  $0.457$ 
B)  $2.248$ 
C)  $2.789$ 
D)  $3.059$ 
E) 4 $.237$ 
A)  $0.457$ 
B)  $2.248$ 
C)  $2.789$ 
D)  $3.059$ 
E) 4 $.237$

Question 7

Using Simpson's Rule with n = 4, the approximated value of $\int _ { \frac { 3 \pi } { 2 } } ^ { 2 \pi } \frac { \cos x } { x } d x,$ to three decimal places, is

Accepted Answer

A) 0.148 
B) 0.176 
C) 0.227 
D) 0.359 
E) 0.237 
A) 0.148 
B) 0.176 
C) 0.227 
D) 0.359 
E) 0.237

Question 8

Using Simpson's Rule with n = 4, the approximated value of $\int _ { 0 } ^ { 1 } e ^ { - x ^ { 2 } } d x,$ to three decimal places, is

Accepted Answer

A)  $0.747$ 
B)  $0.176$ 
C)  $0.285$ 
D)  $0.359$ 
E)  $0.237$ 
A)  $0.747$ 
B)  $0.176$ 
C)  $0.285$ 
D)  $0.359$ 
E)  $0.237$

Question 9

The integral $\int \frac { 1 } { \sqrt { \left( 4 x ^ { 2 } - 1 \right) ^ { 3 } } } d x$ is

Accepted Answer

A)  $\frac { x } { \sqrt { 4 x ^ { 2 } - 1 } } + C$ 
B)  $- \frac { x } { \sqrt { 4 x ^ { 2 } - 1 } } + C$ 
C)  $- \frac { 2 x } { \sqrt { 4 x ^ { 2 } - 1 } } + C$ 
D)  $\frac { 2 x } { \sqrt { 4 x ^ { 2 } - 1 } } + C$ 
E)  $\frac { x } { 2 \sqrt { 4 x ^ { 2 } - 1 } } + C$ 
A)  $\frac { x } { \sqrt { 4 x ^ { 2 } - 1 } } + C$ 
B)  $- \frac { x } { \sqrt { 4 x ^ { 2 } - 1 } } + C$ 
C)  $- \frac { 2 x } { \sqrt { 4 x ^ { 2 } - 1 } } + C$ 
D)  $\frac { 2 x } { \sqrt { 4 x ^ { 2 } - 1 } } + C$ 
E)  $\frac { x } { 2 \sqrt { 4 x ^ { 2 } - 1 } } + C$

The integral $\int \frac { 1 } { ( x + 2 ) \left( x ^ { 2 } + 1 \right) } d x$ is

The integral $\int \frac { 1 } { x ^ { 2 } + 2 x - 15 } d x$ is

The integral $\int \frac { 1 } { 4 x ^ { 2 } - 12 x + 5 } d x$ is

The integral $\int \cos ^ { - 1 } x d x$ is

Using Simpson's Rule with n = 4, the approximated value of $\int _ { 0 } ^ { 2 } \frac { 1 } { x + 1 } d x,$ to three decimal places, is

Using Simpson's Rule with n = 4, the approximated value of $\int _ { 1 } ^ { 2 } \frac { e ^ { x } } { x } d x,$ to three decimal places, is

Using Simpson's Rule with n = 4, the approximated value of $\int _ { \frac { 3 \pi } { 2 } } ^ { 2 \pi } \frac { \cos x } { x } d x,$ to three decimal places, is

Using Simpson's Rule with n = 4, the approximated value of $\int _ { 0 } ^ { 1 } e ^ { - x ^ { 2 } } d x,$ to three decimal places, is

The integral $\int \frac { 1 } { \sqrt { \left( 4 x ^ { 2 } - 1 \right) ^ { 3 } } } d x$ is

Preparing for Calculus

Limits and Continuity

The Derivative

More About Derivatives

Applications of the Derivative

The Integral

Applications of the Integral

Infinite Series

Parametric Equations; Polar Equations

Vectors; Lines, Planes, and Quadric Surfaces in Space

Vector Functions

Functions of Several Variables

Directional Derivatives, Gradients, and Extrema

Multiple Integrals

Vector Calculus

Differential Equations

Filters

Exam 8: Techniques of Integration

The integral ∫1(x+2)(x2+1)dx\int \frac { 1 } { ( x + 2 ) \left( x ^ { 2 } + 1 \right) } d x∫(x+2)(x2+1)1​dx is

The integral ∫1x2+2x−15dx\int \frac { 1 } { x ^ { 2 } + 2 x - 15 } d x∫x2+2x−151​dx is

The integral ∫14x2−12x+5dx\int \frac { 1 } { 4 x ^ { 2 } - 12 x + 5 } d x∫4x2−12x+51​dx is

The integral ∫cos⁡−1xdx\int \cos ^ { - 1 } x d x∫cos−1xdx is

Using Simpson's Rule with n = 4, the approximated value of ∫021x+1dx,\int _ { 0 } ^ { 2 } \frac { 1 } { x + 1 } d x,∫02​x+11​dx, to three decimal places, is

Using Simpson's Rule with n = 4, the approximated value of ∫12exxdx,\int _ { 1 } ^ { 2 } \frac { e ^ { x } } { x } d x,∫12​xex​dx, to three decimal places, is

Using Simpson's Rule with n = 4, the approximated value of ∫3π22πcos⁡xxdx,\int _ { \frac { 3 \pi } { 2 } } ^ { 2 \pi } \frac { \cos x } { x } d x,∫23π​2π​xcosx​dx, to three decimal places, is

Using Simpson's Rule with n = 4, the approximated value of ∫01e−x2dx,\int _ { 0 } ^ { 1 } e ^ { - x ^ { 2 } } d x,∫01​e−x2dx, to three decimal places, is

The integral ∫1(4x2−1)3dx\int \frac { 1 } { \sqrt { \left( 4 x ^ { 2 } - 1 \right) ^ { 3 } } } d x∫(4x2−1)3​1​dx is

Preparing for Calculus

Limits and Continuity

The Derivative

More About Derivatives

Applications of the Derivative

The Integral

Applications of the Integral

Infinite Series

Parametric Equations; Polar Equations

Vectors; Lines, Planes, and Quadric Surfaces in Space

Vector Functions

Functions of Several Variables

Directional Derivatives, Gradients, and Extrema

Multiple Integrals

Vector Calculus

Differential Equations

Filters

The integral $\int \frac { 1 } { ( x + 2 ) \left( x ^ { 2 } + 1 \right) } d x$ is

The integral $\int \frac { 1 } { x ^ { 2 } + 2 x - 15 } d x$ is

The integral $\int \frac { 1 } { 4 x ^ { 2 } - 12 x + 5 } d x$ is

The integral $\int \cos ^ { - 1 } x d x$ is

Using Simpson's Rule with n = 4, the approximated value of $\int _ { 0 } ^ { 2 } \frac { 1 } { x + 1 } d x,$ to three decimal places, is

Using Simpson's Rule with n = 4, the approximated value of $\int _ { 1 } ^ { 2 } \frac { e ^ { x } } { x } d x,$ to three decimal places, is

Using Simpson's Rule with n = 4, the approximated value of $\int _ { \frac { 3 \pi } { 2 } } ^ { 2 \pi } \frac { \cos x } { x } d x,$ to three decimal places, is

Using Simpson's Rule with n = 4, the approximated value of $\int _ { 0 } ^ { 1 } e ^ { - x ^ { 2 } } d x,$ to three decimal places, is

The integral $\int \frac { 1 } { \sqrt { \left( 4 x ^ { 2 } - 1 \right) ^ { 3 } } } d x$ is