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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 \le x \le 1
0
≤
x
≤
1
. Determine the area of the region 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
. [IIT JEE 1997]
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