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Mathematics
Problem
Which definite integral represents the exact area of the region bounded by the line
x
=
3
y
+
2
x = 3y + 2
x
=
3
y
+
2
, the parabola
x
=
y
2
x = y^{2}
x
=
y
2
, and the horizontal lines
y
=
0
y = 0
y
=
0
and
y
=
3
y = 3
y
=
3
? a)
∫
0
3
(
y
2
−
(
3
y
+
2
)
)
d
y
\displaystyle \int_{0}^{3} \bigl(y^{2}-(3y+2)\bigr)\,dy
∫
0
3
(
y
2
−
(
3
y
+
2
)
)
d
y
b)
∫
0
3
(
3
y
+
2
−
y
2
)
d
y
\displaystyle \int_{0}^{3} (3y + 2 - y^{2})\,dy
∫
0
3
(
3
y
+
2
−
y
2
)
d
y
c)
∫
0
3
(
3
y
+
2
−
y
2
)
d
x
\displaystyle \int_{0}^{3} (3y + 2 - y^{2})\,dx
∫
0
3
(
3
y
+
2
−
y
2
)
d
x
d)
∫
2
11
(
3
y
+
2
−
y
2
)
d
y
\displaystyle \int_{2}^{11} (3y + 2 - y^{2})\,dy
∫
2
11
(
3
y
+
2
−
y
2
)
d
y
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