Question 1

Evaluate the integral.
-$$\int _ { 0 } ^ { \pi } \sin 9 t \cos 8 t d t$$

Accepted Answer

A)  $\frac { 1 } { 17 }$ 
B)  $\frac { 9 } { 17 }$ 
C)  $\frac { 19 } { 17 }$ 
D)  $\frac { 18 } { 17 }$ 
A)  $\frac { 1 } { 17 }$ 
B)  $\frac { 9 } { 17 }$ 
C)  $\frac { 19 } { 17 }$ 
D)  $\frac { 18 } { 17 }$

Question 2

Evaluate the integral.
-$$\int 9 \sec ^ { 4 } x d x$$

Accepted Answer

A)  $3 \tan ^ { 3 } x + C$ 
B)  $- 3 \tan ^ { 3 } x + C$ 
C)  $9 ( \sec x + \tan x ) ^ { 5 } + C$ 
D)  $9 \tan x + 3 \tan ^ { 3 } x + C$ 
A)  $3 \tan ^ { 3 } x + C$ 
B)  $- 3 \tan ^ { 3 } x + C$ 
C)  $9 ( \sec x + \tan x ) ^ { 5 } + C$ 
D)  $9 \tan x + 3 \tan ^ { 3 } x + C$

Question 3

Use integration by parts to establish a reduction formula for the integral.
-$$\int \cot ^ { n } x d x , n \neq 1$$

Accepted Answer

A)  $\int \cot ^ { n } x d x = \frac { - 1 } { n - 1 } \cot ^ { n - 1 } x - \int \cot ^ { n - 2 } x d x$ 
B)  $\int \cot ^ { n } x d x = \frac { - 1 } { n - 1 } \cot ^ { n - 2 } x - \int \cot ^ { n - 1 } x d x$ 
C)  $\int \cot ^ { n } x d x = \frac { 1 } { n - 1 } \cot ^ { n - 1 } x + \int \cot ^ { n - 1 } x d x$ 
D)  $\int \cot ^ { n } x d x = - \cot ^ { n - 1 } x + \frac { 1 } { n - 1 } \int \cot ^ { n - 2 } x d x$ 
A)  $\int \cot ^ { n } x d x = \frac { - 1 } { n - 1 } \cot ^ { n - 1 } x - \int \cot ^ { n - 2 } x d x$ 
B)  $\int \cot ^ { n } x d x = \frac { - 1 } { n - 1 } \cot ^ { n - 2 } x - \int \cot ^ { n - 1 } x d x$ 
C)  $\int \cot ^ { n } x d x = \frac { 1 } { n - 1 } \cot ^ { n - 1 } x + \int \cot ^ { n - 1 } x d x$ 
D)  $\int \cot ^ { n } x d x = - \cot ^ { n - 1 } x + \frac { 1 } { n - 1 } \int \cot ^ { n - 2 } x d x$

Question 4

Evaluate the integral.
-$$\int \frac { \cot ^ { 3 } x } { 7 } d x$$

Accepted Answer

A)  $\frac { 1 } { 14 } \cot ^ { 2 } x + \ln | \sin x | + C$ 
B)  $\frac { 1 } { 28 } \cot ^ { 4 } x + C$ 
C)  $\frac { 1 } { 28 } \cot ^ { 4 } x \sec x + C$ 
D)  $- \frac { 1 } { 14 } \cot ^ { 2 } x - \frac { 1 } { 7 } \ln | \sin x | + C$ 
A)  $\frac { 1 } { 14 } \cot ^ { 2 } x + \ln | \sin x | + C$ 
B)  $\frac { 1 } { 28 } \cot ^ { 4 } x + C$ 
C)  $\frac { 1 } { 28 } \cot ^ { 4 } x \sec x + C$ 
D)  $- \frac { 1 } { 14 } \cot ^ { 2 } x - \frac { 1 } { 7 } \ln | \sin x | + C$

Evaluate the integral. - $\int _ { 0 } ^ { \pi } \sin 9 t \cos 8 t d t$

Evaluate the integral. - $\int 9 \sec ^ { 4 } x d x$

Use integration by parts to establish a reduction formula for the integral. - $\int \cot ^ { n } x d x , n \neq 1$

Evaluate the integral. - $\int \frac { \cot ^ { 3 } x } { 7 } d x$

Functions

Limits and Derivatives

Differentiation

Applications of Derivatives

Integration

Applications of Definite Integrals

Integrals and Transcendental Functions

First-Order Differential Equations

Infinite Sequences and Series

Filters

Exam 8: Techniques of Integration

Evaluate the integral. - ∫0πsin⁡9tcos⁡8tdt\int _ { 0 } ^ { \pi } \sin 9 t \cos 8 t d t∫0π​sin9tcos8tdt

Evaluate the integral. - ∫9sec⁡4xdx\int 9 \sec ^ { 4 } x d x∫9sec4xdx

Use integration by parts to establish a reduction formula for the integral. - ∫cot⁡nxdx,n≠1\int \cot ^ { n } x d x , n \neq 1∫cotnxdx,n=1

Evaluate the integral. - ∫cot⁡3x7dx\int \frac { \cot ^ { 3 } x } { 7 } d x∫7cot3x​dx