Question 1

Integrate  dx.
A) x  -  + C
B) -x  +  + C
C) x  +  + C
D) x  -  + C
E) x  + 2

Accepted Answer

D

Question 2

Integrate  dx.
A) x cos x - sin x + C
B) x sin x + cos x + C
C) -x cos x + sin x + C
D) x sin x - cos x + C
E) -x sin x + cos x + C

Accepted Answer

B

Question 3

Find  dx.
A) 1 - 
B) -1
C)  - 1
D) 
E) -1 -

Accepted Answer

A

Question 4

Integrate  dx.
A)  ln x +   + C
B)  ln x -   + C
C)  ln x +  x + C
D)  ln x -  x + C
E)  ln x -   + C

Accepted Answer

The answer of Integrate  dx.
A)  ln x +...

Question 5

Integrate  dx.
A)  + 
B)  - 
C)  - 
D)  + 
E)

Accepted Answer

The answer of Integrate  dx.
A)  + 
B) ...

Question 6

Integrate  ln(5x) dx.
A)  ln(5x) -   + C
B)  ln(5x) +   + C
C)  ln(5x) +   + C
D)  ln(5x) -   + C
E)  ln(5x) -   + C

Accepted Answer

The answer of Integrate  ln(5x) dx.
A)  ln(5x) -...

Question 7

Evaluate  .
A)   (  ) + C
B)   (  ) +  + C
C)   (  ) -  + C
D)   (  ) + ln(1 -  ) + C
E)   (  ) + 2x  (  ) + C

Accepted Answer

The answer of Evaluate  .
A)   ( ...

Question 8

Integrate  .
A)   (2  - 2x - 1) + C
B)   (2  + 2x - 1) + C
C)   (2  - 2x + 1) + C
D)   (2  + 2x + 1) + C
E)   (2  - 2x + 1) + C

Accepted Answer

The answer of Integrate  .
A)   (2 ...

Question 9

Integrate  dx.
A) -  -  +  + C
B)  -  -  + C
C) -  +  -  + C
D) -  -  -  + C
E)  +  -  + C

Accepted Answer

The answer of Integrate  dx.
A) -  - ...

Question 10

Evaluate the integral  t dt.
A)  + 
B)  - 
C)  - 
D)  + 
E)  +

Accepted Answer

The answer of Evaluate the integral  t dt.
A) ...

Question 11

Integrate 
A)  x  x -  x +  sin 2x + C
B)  x  x +  x +  sin 2x + C
C)  x  x -  x -  sin 2x + C
D)  x  x +  x -  sin 2x + C
E)  x  x -  x +  cos 2x + C

Accepted Answer

The answer of Integrate 
A)  x  x -...

Question 12

Evaluate  .
A) x  (x) -  ln(1 +  ) + C
B)  + C
C) x  (x) -  ln(1 +  ) + C
D) arc  + C
E) ln  + C

Accepted Answer

The answer of Evaluate  .
A) x  (x) -...

Question 13

Evaluate the integral  sin 4x dx.
A)  (3 sin 4x - 4 cos 4x) + C
B)  (4 sin 4x - 3 cos 4x) + C
C)  (3 sin 4x + 4 cos 4x) + C
D)  (4 sin 4x + 3 cos 4x) + C
E)  (3 sin 4x - 4 cos 4x) + C

Accepted Answer

The answer of Evaluate the integral  sin 4x dx.
A)...

Question 14

Integrate  dx.
A) 6 - 2e
B) 4e - 6
C) e + 3
D) 4e - 3
E) 2e - 1

Accepted Answer

The answer of Integrate  dx.
A) 6 - 2e
B) 4e...

Question 15

Evaluate the integral  dx.
A)  - 
B)  + 
C)  + 
D)  - 
E)

Accepted Answer

The answer of Evaluate the integral  dx.
A)  -...

Question 16

Integrate  dx.
A) 6 - 2e
B)  - 
C)  - 
D)  + 
E) 2  + 6

Accepted Answer

The answer of Integrate  dx.
A) 6 - 2e
B) ...

Question 17

Integrate 
A)   ln x -   + C
B)   ln x +   + C
C)   ln x -   + C
D)   ln x +   + C
E)   ln x -   + C

Accepted Answer

The answer of Integrate 
A)   ln x -...

Question 18

Evaluate  dx.
A) 8  + 4
B) 4
C) 8 -5
D) -4
E) 3

Accepted Answer

The answer of Evaluate  dx.
A) 8  + 4
B)...

Question 19

Find a reduction formula for = and use it to evaluate I₃ = dx. A) = x - n , - 3x + 6x ln x - 6x + C B) = x + n , + 3x + 6x ln x + 6x + C C) = x - , - x + x ln x - x + C D) = x + , - x + x ln x - x + C E) = x - n , - 3x - 6x ln x + 6x + C

Accepted Answer

The answer of Find a reduction formula for  =...

Question 20

Find a reduction formula for I_n = and use it to evaluate I₄ = . dx A) = - , = + C B) = + , = + C C) = - n , = + C D) = + n , = + C E) = + , = + C

Accepted Answer

The answer of Find a reduction formula for I_n =...

Quiz 7: Techniques of Integration

Integrate dx.

Integrate dx.

Find dx.

Integrate dx.

Integrate dx.

Integrate ln(5x) dx.

Evaluate .

Integrate .

Integrate dx.

Evaluate the integral t dt.

Integrate

Evaluate .

Evaluate the integral sin 4x dx.

Integrate dx.

Evaluate the integral dx.

Integrate dx.

Integrate

Evaluate dx.

Find a reduction formula for = and use it to evaluate I3 = dx.

Find a reduction formula for In = and use it to evaluate I4 = . dx

Find a reduction formula for = and use it to evaluate I₃ = dx.

Find a reduction formula for I_n = and use it to evaluate I₄ = . dx