# Final Exam.MATH 106(1434)

```Majmaah University
College of Engineering
Total Marks: 40
Final Exam.
Examiner: Dr. Tarek Nabil Ahmed
Math. ‘106’
Integral Calculus II
Time: 3 hour , 23/2/1434
Question 1: Evaluate the following integrals:

2
6
2
(1)  cos x sin x dx ,
-

(2) 
x2
2 - x3
dx,
(3)  23 4 x dx,
2
(4) 
x2
5  x6
(5)  cosecx dx,
dx,
(6)  sin 3 x cos 7 x dx ,

(7 ) 
4  x2
x
2
2 siny
dx,
4
(10)  cot xdx,
(8)  
0 0
e
1
1- x
2
dx ,
3 21
(11)    3x 2 z dz dy dx
100
(13)  cos(lnx) dx ,
(14) 
e 2x
1 - e 4x
dx,
(9)  lnx dx,
1
(12) 
1
dx,
1 - cosx
(15)  x tan -1x dx
)20 marks)
Question 2: Find the area of the region bounded by the parabola y  x
yx2
line
2 and the
)4 marks)
Question 3: Find the volume of the solid generated by revolving the region R
bounded by the graphs of the equations x 2  y  2 and 2y - x - 2  0
and the vertical lines x=0 and x=1 about the x-axis.
)4 marks)
x3 1

Question 4: Find the length of the arc of the curve y 
from x=1 to x=2
6 2x
)4 marks)
Question 5: Use the triple integration to find the volume
x y z
   1, x  0, y  0, z  0
a b c
)4 marks)
Question 6: Use the double integration to find the area of the region D bounded by
x2  1
2
the curves
yx ,
y
2
)4 marks)
With my best wishes
```