Test:
Integration III - Challenging
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Question 1:
Solve integral
∫
(
5
cos
(
x
)
)
d
(
cos
(
x
)
)
A
F
(
x
)
=
5
cos
(
x
)
ln
(
5
)
B
F
(
x
)
=
5
cos
(
x
)
+
C
C
F
(
x
)
=
5
cos
(
x
)
ln
(
5
)
+
C
D
F
(
x
)
=
5
cos
(
x
)
+
C
Question 2:
Find the antiderivative of the function
f
(
x
)
=
cos
2
(
7
x
)
A
F
(
x
)
=
1
2
(
x
+
1
14
×
sin
(
14
x
)
)
+
C
B
F
(
x
)
=
1
2
(
x
+
sin
(
x
)
)
+
C
C
F
(
x
)
=
1
2
(
x
+
sin
(
14
x
)
)
+
C
D
F
(
x
)
=
x
+
1
14
×
sin
(
14
x
)
+
C
Question 3:
Find the antiderivative of the function
f
(
x
)
=
8
1
+
9
x
2
A
F
(
x
)
=
8
arctan
(
3
x
)
+
C
B
F
(
x
)
=
8
3
arctan
(
x
3
)
+
C
C
F
(
x
)
=
1
3
arctan
(
3
x
)
+
C
D
F
(
x
)
=
8
3
arctan
(
3
x
)
+
C
Question 4:
Calculate
∫
0
π
(
1
cos
2
(
x
4
)
)
d
x
A
5
B
4
C
-
3
D
π
Question 5:
Find the antiderivative of the function
f
(
x
)
=
5
x
+
1
that passes via point
(
2
;
5
)
A
F
(
x
)
=
5
x
2
2
+
x
B
F
(
x
)
=
5
x
2
2
+
x
+
7
C
F
(
x
)
=
5
x
2
2
+
x
-
3
D
F
(
x
)
=
5
x
2
2
+
x
-
7
Question 6:
Find the antiderivative of the function
f
(
x
)
=
7
x
+
2
that passes via point
(
0
;
0
)
A
F
(
x
)
=
7
x
ln
(
7
)
+
2
x
+
1
ln
(
7
)
B
F
(
x
)
=
7
x
ln
(
7
)
+
2
x
+
3
ln
(
7
)
C
F
(
x
)
=
7
x
ln
(
7
)
+
x
-
1
ln
(
7
)
D
F
(
x
)
=
7
x
ln
(
7
)
+
2
x
-
1
ln
(
7
)
Question 7:
Calculate the area of the figure defined by
y
=
cos
(
x
)
,
x
=
0
,
x
=
π
6
A
2
π
B
π
2
C
1
2
D
5
π
2
Question 8:
Find the formula for the area of the shaded region:
A
S
=
∫
0
2
(
x
)
d
x
B
S
=
-
∫
0
4
(
x
)
d
x
C
S
=
∫
0
4
|
x
|
d
x
D
S
=
∫
0
4
(
x
)
d
x
Question 9:
Calculate the area of the figure defined by
y
=
x
2
and
y
=
x
A
1
4
B
1
C
6
D
1
6
Question 10:
Calculate the area of the figure defined by
y
=
x
,
x
=
5
and
y
=
0
A
12
B
13.5
C
10
D
12.5
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