Test:
Integration I - Ambitious
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Question 1:
Find the antiderivative of the function
f
(
x
)
=
(
x
-
1
)
2
A
F
(
x
)
=
x
3
3
-
x
2
2
+
x
+
C
B
F
(
x
)
=
x
3
3
+
x
+
C
C
F
(
x
)
=
x
3
3
-
x
2
+
x
+
C
D
F
(
x
)
=
x
3
3
-
x
2
+
x
Question 2:
Find the antiderivative of the function
f
(
x
)
=
(
e
x
)
2
A
F
(
x
)
=
e
x
2
+
C
B
F
(
x
)
=
e
2
x
+
C
C
F
(
x
)
=
e
2
x
2
D
F
(
x
)
=
e
2
x
2
+
C
Question 3:
Find the antiderivative of the function
f
(
x
)
=
1
2
x
+
4
x
3
A
F
(
x
)
=
1
2
ln
|
x
|
+
x
4
+
C
B
F
(
x
)
=
1
2
ln
|
x
|
+
x
4
C
F
(
x
)
=
ln
|
x
|
+
x
4
+
C
D
F
(
x
)
=
1
2
ln
|
x
|
+
x
4
4
+
C
Question 4:
Find the antiderivative of the function
f
(
x
)
=
2
sin
(
x
)
+
7
cos
(
x
)
A
F
(
x
)
=
2
cos
(
x
)
+
7
sin
(
x
)
+
C
B
F
(
x
)
=
-
2
cos
(
x
)
+
7
sin
(
x
)
+
C
C
F
(
x
)
=
-
2
cos
(
x
)
+
7
sin
(
x
)
D
F
(
x
)
=
-
2
cos
(
x
)
-
7
sin
(
x
)
+
C
Question 5:
Find the antiderivative of the function
f
(
x
)
=
1
16
+
x
2
A
F
(
x
)
=
1
4
arctan
(
x
4
)
B
F
(
x
)
=
1
4
arctan
(
x
4
)
+
C
C
F
(
x
)
=
1
4
arctan
(
x
)
+
C
D
F
(
x
)
=
1
2
arctan
(
x
2
)
+
C
Question 6:
Calculate
∫
0
2
π
3
(
cos
(
3
x
4
)
)
d
x
A
1
B
3
4
C
0
D
4
3
Question 7:
Calculate
∫
0
5
(
(
3
5
x
)
2
-
5
x
)
d
x
A
47.5
B
-
47.5
C
-
50.5
D
50.5
Question 8:
Calculate
∫
1
2
(
2
x
-
3
)
d
x
A
-
1
B
2
ln
(
2
)
C
2
ln
(
2
)
-
3
D
0
Question 9:
Calculate the area of the figure defined by
y
=
x
2
and
y
=
4
A
3
32
B
32
3
C
4
D
1
Question 10:
Calculate the area of the figure defined by
y
=
2
x
-
4
,
x
=
5
and
y
=
0
A
12
B
9
C
3
D
25
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