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Mathematics
Problem
The region in the
x
y
xy
x
y
-plane is bounded by the graphs of
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 gives the exact area of this region? 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)
∫
0
2
(
(
y
+
2
)
−
y
2
)
d
y
\displaystyle \int_{0}^{2} \bigl((y+2) - y^{2}\bigr)\,dy
∫
0
2
(
(
y
+
2
)
−
y
2
)
d
y
c)
∫
−
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
d)
∫
−
1
2
(
y
+
2
)
d
y
\displaystyle \int_{-1}^{2} (y+2)\,dy
∫
−
1
2
(
y
+
2
)
d
y
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