Question 1

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

Accepted Answer

A)    117\frac { 1 } { 17 }171​ 
B)    917\frac { 9 } { 17 }179​ 
C)    1917\frac { 19 } { 17 }1719​ 
D)    1817\frac { 18 } { 17 }1718​E) A) and D)
F) B) and D)

Question 2

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

Accepted Answer

A)    114cot⁡2x+ln⁡∣sin⁡x∣+C\frac { 1 } { 14 } \cot ^ { 2 } x + \ln | \sin x | + C141​cot2x+ln∣sinx∣+C 
B)    128cot⁡4x+C\frac { 1 } { 28 } \cot ^ { 4 } x + C281​cot4x+C 
C)    128cot⁡4xsec⁡x+C\frac { 1 } { 28 } \cot ^ { 4 } x \sec x + C281​cot4xsecx+C 
D)    −114cot⁡2x−17ln⁡∣sin⁡x∣+C- \frac { 1 } { 14 } \cot ^ { 2 } x - \frac { 1 } { 7 } \ln | \sin x | + C−141​cot2x−71​ln∣sinx∣+CE) B) and C)
F) A) and C)

Question 3

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

Accepted Answer

A)    3tan⁡3x+C3 	an ^ { 3 } x + C3tan3x+C 
B)    −3tan⁡3x+C- 3 	an ^ { 3 } x + C−3tan3x+C 
C)    9(sec⁡x+tan⁡x) 5+C9 ( \sec x + 	an x )  ^ { 5 } + C9(secx+tanx) 5+C 
D)    9tan⁡x+3tan⁡3x+C9 	an x + 3 	an ^ { 3 } x + C9tanx+3tan3x+CE) C) and D)
F) B) and C)

Question 4

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

Accepted Answer

A)    ∫cot⁡nxdx=−1n−1cot⁡n−1x−∫cot⁡n−2xdx\int \cot ^ { n } x d x = \frac { - 1 } { n - 1 } \cot ^ { n - 1 } x - \int \cot ^ { n - 2 } x d x∫cotnxdx=n−1−1​cotn−1x−∫cotn−2xdx 
B)    ∫cot⁡nxdx=−1n−1cot⁡n−2x−∫cot⁡n−1xdx\int \cot ^ { n } x d x = \frac { - 1 } { n - 1 } \cot ^ { n - 2 } x - \int \cot ^ { n - 1 } x d x∫cotnxdx=n−1−1​cotn−2x−∫cotn−1xdx 
C)    ∫cot⁡nxdx=1n−1cot⁡n−1x+∫cot⁡n−1xdx\int \cot ^ { n } x d x = \frac { 1 } { n - 1 } \cot ^ { n - 1 } x + \int \cot ^ { n - 1 } x d x∫cotnxdx=n−11​cotn−1x+∫cotn−1xdx 
D)    ∫cot⁡nxdx=−cot⁡n−1x+1n−1∫cot⁡n−2xdx\int \cot ^ { n } x d x = - \cot ^ { n - 1 } x + \frac { 1 } { n - 1 } \int \cot ^ { n - 2 } x d x∫cotnxdx=−cotn−1x+n−11​∫cotn−2xdxE) A) and D)
F) All of the above

Exam 8: Techniques of Integration

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

Exam 8: Techniques of Integration

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified

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

Correct Answer
verified