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Mathematics
Problem
Which definite integral represents the exact area of the region bounded by the graph of
f
(
x
)
=
3
x
+
1
f(x)=3x+1
f
(
x
)
=
3
x
+
1
, the
x
x
x
-axis, and the vertical lines
x
=
0
x=0
x
=
0
and
x
=
2
x=2
x
=
2
? a)
∫
2
0
(
3
x
+
1
)
d
x
\displaystyle \int_{2}^{0} (3x+1)\,dx
∫
2
0
(
3
x
+
1
)
d
x
b)
1
2
∫
0
2
(
3
x
+
1
)
d
x
\displaystyle \tfrac12\displaystyle \int_{0}^{2} (3x+1)\,dx
2
1
∫
0
2
(
3
x
+
1
)
d
x
c)
∫
0
2
(
3
x
+
1
)
d
x
\displaystyle \int_{0}^{2} (3x+1)\,dx
∫
0
2
(
3
x
+
1
)
d
x
d)
∫
0
2
(
3
x
+
1
)
d
x
+
C
\displaystyle \int_{0}^{2} (3x+1)\,dx + C
∫
0
2
(
3
x
+
1
)
d
x
+
C
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