MATH 1432 - EMCF 4
Due before 11:59 pm on the due date indicated at CASA.
Log into CASA and access the answer sheet by clicking on the EMCF tab.
Choice F is “None of the above” on all questions.
1.
 xe
x
dx 
a.  xe  x  e  x  C
b. xe x  e x  C
c.  xe  x  e  x  C
d.  xe  x  x  C
2. If we use integration by parts to evaluate
 x arctan  x  dx then we should choose
1
, dv  xdx
1 x 2
b. u  x, dv  arctan x dx
a. u 


u  arctan  x  , dv  xdx
c. u  x arctan x , dv  dx
d.
3.
1
 0 x arctan x dx 

a.
4
b.   2

c.
2
 2
d.
2
 2
4
e.
4.
 x ln x
5
dx 
(hint : simplify the ln x 5 first)
a. x 2 ln x 4  C
b.
5x2
5x2
ln x 
C
2
4
c.
5x2
5x2
ln x 
C
2
4
5x2
C
d. 5 x ln x 
2
2
1
5.
 x ln  2x  1 dx 
0
1
ln  3
4
1
ln  3  1
b.
4
3
ln  3  1
c.
8
3
ln  3
d.
8
a.




6. Calculate the following integral:
 tan
4
xdx
1 3
tan x  tan x  x  C
3
1 3
b.
tan x  tan x  x  C
3
1 3
c.
tan x  tan x  x  C
3
1 3
tan x  tan x  C
d.
3
a.
7. Calculate the following integral:
1 4
tan x  C
4
1 2
b.
tan x  ln | cos x | C
2
1 2
c.
tan x  ln | cos x | C
2
d. tan 2 x  ln | cos x | C
a.
8.
 sin x cos
3
4
xdx 
1
1 4
sin x  sin 6 x  C
6
4
1
1 5
b.
cos x  cos7 x  C
7
5
a.
 tan xdx
3
1
1
c.  cos5 x  cos7 x  C
5
7
1
1 5
d.
sin x  sin 7 x  C
7
5
9.
 sec
4
xdx 
1 3
tan x  tan x  C
3
1 5
1
tan x  tan 7 x  C
b.
5
7
1
1
c.
tan 2 x  tan 4 x  C
2
4
d. x  tan x  C
a.
10.  sec 4 x tan xdx 
1 3
tan x  tan x  C
3
1
1
tan 2 x  tan 4 x  C
b.
2
4
1 5
1
tan x  tan 7 x  C
c.
5
7
d. x  tan x  C
a.
11.  sec 4 x tan 4 xdx 
1 5
1
tan x  tan 7 x  C
5
7
1 3
b.
tan x  tan x  C
3
1
1
tan 2 x  tan 4 x  C
c.
2
4
d. x  tan x  C
a.
12.  sin(5 x) sin(3x)dx 
1
1
sin( 2 x)  sin(8 x)  C
4
16
1
1
b.  sin(2 x)  sin(8 x)  C
4
16
1
1
sin(2 x)  sin(8 x)  C
c.
2
2
1
1
d.  sin(2x)  sin(8x)  C
2
2
a.
13. Calculate the given integral:  sec  5x  dx
a.
b.
c.
d.
e.
1
ln tan(5 x)  C
5
1
ln sec(5 x)  tan(5 x)  C
5
1
ln cos(5 x)  C
5
1
sec(5 x) tan(5 x)  C
5
1 2
tan  5 x   C
5
14. Evaluate the integral:
 sin  3x  cos  3x  dx
3
1 4
sin 3x cos 2 3x  C
8
1 4
b.
sin 3x  C
4
c. 3sin 2 3x (3cos 2 3x  sin 2 3x)  C
1
d.
sin 4 3x  C
12
a.