Test:
Integration I - Challenging
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Question 1:
Solve integral
∫
(
1
1
-
sin
2
(
3
x
)
)
d
(
sin
(
3
x
)
)
A
F
(
x
)
=
sin
(
3
x
)
+
C
B
F
(
x
)
=
arcsin
(
sin
(
3
x
)
)
+
C
C
F
(
x
)
=
s
i
n
(
arcsin
(
3
x
)
)
+
C
D
F
(
x
)
=
arcsin
(
sin
(
3
x
)
)
Question 2:
Find the antiderivative of the function
f
(
x
)
=
sin
2
(
5
x
)
A
F
(
x
)
=
1
2
(
x
-
sin
(
10
x
)
)
+
C
B
F
(
x
)
=
sin
3
(
5
x
)
3
+
C
C
F
(
x
)
=
x
-
1
10
×
sin
(
10
x
)
+
C
D
F
(
x
)
=
1
2
(
x
-
1
10
×
sin
(
10
x
)
)
+
C
Question 3:
Find the antiderivative of the function
f
(
x
)
=
1
1
+
5
x
2
A
F
(
x
)
=
5
arccot
(
5
x
)
+
C
B
F
(
x
)
=
1
5
arccot
(
5
x
)
+
C
C
F
(
x
)
=
1
5
arccot
(
x
)
+
C
D
F
(
x
)
=
5
arccot
(
5
x
)
+
C
Question 4:
Calculate
∫
0
π
(
cos
(
x
2
)
)
d
x
A
π
B
2
C
4
D
1
Question 5:
Find the antiderivative of the function
f
(
x
)
=
8
x
3
+
3
x
2
that passes via point
(
1
;
5
)
A
F
(
x
)
=
2
x
4
+
x
3
+
5
B
F
(
x
)
=
2
x
4
+
x
3
+
C
C
F
(
x
)
=
2
x
4
+
x
3
D
F
(
x
)
=
2
x
4
+
x
3
+
2
Question 6:
Find the antiderivative of the function
f
(
x
)
=
e
x
+
3
hat passes via point
(
0
;
-
7
)
A
F
(
x
)
=
e
x
+
3
x
-
8
B
F
(
x
)
=
e
x
+
3
x
+
8
C
F
(
x
)
=
e
x
+
3
x
+
C
D
F
(
x
)
=
e
x
+
3
x
+
2
Question 7:
Calculate the area of the figure defined by
y
=
x
,
x
=
2
3
,
x
=
8
3
A
10
π
3
B
5
π
3
C
2
π
D
3
π
10
Question 8:
Find the formula for the area of the shaded region:
A
S
=
∫
0
2
π
(
sin
(
x
)
)
d
x
B
S
=
-
∫
0
2
π
(
sin
(
x
)
)
d
x
C
S
=
∫
0
π
(
sin
(
x
)
)
d
x
D
S
=
∫
0
π
(
sin
(
x
)
)
d
x
-
∫
π
2
π
(
sin
(
x
)
)
d
x
Question 9:
Calculate the area of the figure defined by
y
=
x
2
and
y
=
3
x
A
3
B
5
C
4.5
D
9
Question 10:
Calculate the area of the figure defined by
y
=
x
2
,
x
=
4
and
y
=
0
A
6
B
4
C
7
D
2
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