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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
Max
{
x
2
,
(
1
−
x
)
2
,
2
x
(
1
−
x
)
}
f(x) = \text{Max}\{x^2, (1-x)^2, 2x(1-x)\}
f
(
x
)
=
Max
{
x
2
,
(
1
−
x
)
2
,
2
x
(
1
−
x
)}
where
0
≤
x
≤
1
0 \leq x \leq 1
0
≤
x
≤
1
, if the area of the origin bounded by the curves
y
=
f
(
x
)
y = f(x)
y
=
f
(
x
)
,
x
x
x
-axis,
x
=
0
x = 0
x
=
0
and
x
=
1
x = 1
x
=
1
is
p
q
\frac{p}{q}
q
p
then
p
+
q
p + q
p
+
q
.
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