Test:
Integration III - Ambitious
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Question 1:
Find the antiderivative of the function
f
(
x
)
=
(
x
-
3
)
2
A
F
(
x
)
=
x
3
3
-
3
x
2
+
9
x
B
F
(
x
)
=
x
3
3
-
3
x
2
+
9
x
+
C
C
F
(
x
)
=
x
3
-
6
x
2
+
9
x
+
C
D
F
(
x
)
=
x
3
3
-
3
x
2
+
C
Question 2:
Find the antiderivative of the function
f
(
x
)
=
e
6
x
A
F
(
x
)
=
6
e
6
x
+
C
B
F
(
x
)
=
e
x
6
+
C
C
F
(
x
)
=
e
6
x
6
D
F
(
x
)
=
e
6
x
6
+
C
Question 3:
Find the antiderivative of the function
f
(
x
)
=
sin
(
5
x
3
)
A
F
(
x
)
=
-
cos
(
5
x
3
)
+
C
B
F
(
x
)
=
-
3
5
cos
(
5
x
3
)
C
F
(
x
)
=
-
3
5
cos
(
5
x
3
)
+
C
D
F
(
x
)
=
3
5
cos
(
5
x
3
)
+
C
Question 4:
Find the equation of integral for the area of the shaded region:
A
S
=
∫
(
3
x
)
d
x
B
S
=
∫
(
3
x
-
1
)
d
x
C
S
=
∫
(
3
x
+
1
)
d
x
D
S
=
∫
(
3
x
-
7
x
)
d
x
Question 5:
Find the formula for the area of the shaded region:
A
S
=
∫
(
7
x
+
5
)
d
x
B
S
=
∫
(
2
)
d
x
C
S
=
∫
(
2
x
-
1
)
d
x
D
S
=
∫
(
2
x
)
d
x
Question 6:
Find the integral of the function
f
(
x
)
=
1
7
+
x
2
A
F
(
x
)
=
7
arctan
(
x
7
)
+
C
B
F
(
x
)
=
1
7
arctan
(
x
)
+
C
C
F
(
x
)
=
1
7
arctan
(
x
7
)
+
C
D
F
(
x
)
=
1
7
arctan
(
x
7
)
Question 7:
Calculate
∫
1
2
(
4
x
3
+
2
x
)
d
x
A
18
B
16
C
20
D
12
Question 8:
Calculate
∫
0
2
(
x
2
+
1
)
d
x
A
4
B
8
C
5
D
7
Question 9:
Calculate the area of the figure defined by
y
=
x
2
and
y
=
9
A
36
B
9
C
1
36
D
2
Question 10:
Calculate the area of the figure defined by
y
=
x
,
x
=
5
and
y
=
0
A
7
B
12.5
C
14
D
13.5
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