Test:
Integration II - Challenging
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Question 1:
Solve integral
∫
(
1
cos
2
(
e
x
)
)
d
(
e
x
)
A
F
(
x
)
=
e
x
+
C
B
F
(
x
)
=
tan
(
x
)
+
C
C
F
(
x
)
=
tan
(
e
x
)
D
F
(
x
)
=
tan
(
e
x
)
+
C
Question 2:
Find the antiderivative of the function
f
(
x
)
=
cos
2
(
3
x
)
A
F
(
x
)
=
x
+
1
6
×
sin
(
6
x
)
+
C
B
F
(
x
)
=
1
2
(
x
+
sin
(
x
)
)
+
C
C
F
(
x
)
=
1
2
(
x
+
sin
(
6
x
)
)
+
C
D
F
(
x
)
=
1
2
(
x
+
1
6
×
sin
(
6
x
)
)
+
C
Question 3:
Find the antiderivative of the function
f
(
x
)
=
5
1
+
16
x
2
A
F
(
x
)
=
1
4
arctan
(
4
x
)
+
C
B
F
(
x
)
=
4
5
arctan
(
4
x
)
+
C
C
F
(
x
)
=
5
4
arctan
(
4
x
)
+
C
D
F
(
x
)
=
5
arctan
(
4
x
)
+
C
Question 4:
Calculate
∫
0
π
(
sin
(
x
3
)
)
d
x
A
3.5
B
1
C
1.5
D
π
Question 5:
Find the antiderivative of the function
f
(
x
)
=
9
x
2
-
x
that passes via point
(
1
;
1
)
A
F
(
x
)
=
3
x
3
-
x
2
2
-
1
B
F
(
x
)
=
3
x
3
-
x
2
2
-
1.5
C
F
(
x
)
=
3
x
3
-
x
2
2
+
2
D
F
(
x
)
=
3
x
3
-
x
2
2
+
C
Question 6:
Find the antiderivative of the function
f
(
x
)
=
sin
(
x
)
+
cos
(
x
)
that passes via point
(
π
;
0
)
A
F
(
x
)
=
-
cos
(
x
)
+
sin
(
x
)
-
1
B
F
(
x
)
=
-
cos
(
x
)
+
sin
(
x
)
C
F
(
x
)
=
-
cos
(
x
)
+
sin
(
x
)
+
1
D
F
(
x
)
=
-
cos
(
x
)
+
sin
(
x
)
+
C
Question 7:
Calculate the area of the figure defined by
y
=
x
,
x
=
3
,
x
=
9.
A
729
π
B
234
π
C
81
π
D
225
π
Question 8:
Find the formula for the area of the shaded region:
A
S
=
∫
0
π
(
cos
(
x
)
)
d
x
B
S
=
∫
0
π
2
(
cos
(
x
)
)
d
x
-
∫
π
2
3
π
2
(
cos
(
x
)
)
d
x
+
∫
3
π
2
2
π
(
cos
(
x
)
)
d
x
C
S
=
∫
0
2
π
(
cos
(
x
)
)
d
x
D
S
=
-
∫
0
2
π
(
cos
(
x
)
)
d
x
Question 9:
Calculate the area of the figure defined by
y
=
x
2
and
y
=
2
x
A
1
B
3
4
C
4
D
4
3
Question 10:
Calculate the area of the figure defined by
y
=
3
x
,
x
=
2
and
y
=
0
A
4
B
6
C
7
D
2
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