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Mathematics
Mathematics
Problem
Find the definite integral that correctly represents the area of the region enclosed by the curves
x
=
y
2
x = y^{2}
x
=
y
2
and
x
=
5
−
y
x = 5 - y
x
=
5
−
y
for
0
≤
y
≤
2
0 \le y \le 2
0
≤
y
≤
2
. a)
∫
0
2
[
y
2
−
(
5
−
y
)
]
d
y
\displaystyle \int_{0}^{2} \bigl[y^{2} - (5 - y)\bigr]\,dy
∫
0
2
[
y
2
−
(
5
−
y
)
]
d
y
b)
∫
0
21
−
1
2
[
(
5
−
y
)
−
y
2
]
d
y
\displaystyle \int_{0}^{\frac{\sqrt{21}-1}{2}} \bigl[(5 - y) - y^{2}\bigr]\,dy
∫
0
2
21
−
1
[
(
5
−
y
)
−
y
2
]
d
y
c)
∫
0
2
[
(
5
−
y
)
−
y
2
]
d
y
\displaystyle \int_{0}^{2} \bigl[(5 - y) - y^{2}\bigr]\,dy
∫
0
2
[
(
5
−
y
)
−
y
2
]
d
y
d)
∫
0
5
[
(
5
−
y
)
−
y
2
]
d
y
\displaystyle \int_{0}^{5} \bigl[(5 - y) - y^{2}\bigr]\,dy
∫
0
5
[
(
5
−
y
)
−
y
2
]
d
y
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