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Mathematics
Problem
Region R is enclosed by the curves
x
=
y
2
x = y^2
x
=
y
2
and
x
=
y
+
2
x = y + 2
x
=
y
+
2
. Which of the following definite integrals correctly represents the area of R as a single integral? a)
∫
−
1
2
[
y
2
−
(
y
+
2
)
]
d
y
\displaystyle\int_{-1}^{2} \bigl[y^{2} - (y+2)\bigr] \, dy
∫
−
1
2
[
y
2
−
(
y
+
2
)
]
d
y
b)
∫
−
1
2
[
(
y
+
2
)
−
y
2
]
d
y
\displaystyle\int_{-1}^{2} \bigl[(y+2) - y^{2}\bigr] \, dy
∫
−
1
2
[
(
y
+
2
)
−
y
2
]
d
y
c)
∫
1
4
[
x
−
(
x
−
2
)
]
d
x
\displaystyle\int_{1}^{4} \bigl[\sqrt{x} - (x-2)\bigr] \, dx
∫
1
4
[
x
−
(
x
−
2
)
]
d
x
d)
∫
−
1
2
[
(
y
+
2
)
+
y
2
]
d
y
\displaystyle\int_{-1}^{2} \bigl[(y+2) + y^{2}\bigr] \, dy
∫
−
1
2
[
(
y
+
2
)
+
y
2
]
d
y
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