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Mathematics
Mathematics
Problem
Consider the following regions in the plane:
R
1
=
{
(
x
,
y
)
:
0
≤
x
≤
1
and
0
≤
y
≤
1
}
R_1 = \{(x, y) : 0 \le x \le 1 \text{ and } 0 \le y \le 1\}
R
1
=
{(
x
,
y
)
:
0
≤
x
≤
1
and
0
≤
y
≤
1
}
and
R
2
=
{
(
x
,
y
)
:
x
2
+
y
2
≤
4
/
3
}
R_2 = \{(x, y) : x^2 + y^2 \le 4/3\}
R
2
=
{(
x
,
y
)
:
x
2
+
y
2
≤
4/3
}
The area of the region
R
1
∩
R
2
R_1 \cap R_2
R
1
∩
R
2
can be expressed as
a
3
+
b
π
9
\frac{a\sqrt{3} + b\pi}{9}
9
a
3
+
bπ
, where
a
a
a
and
b
b
b
are integers, then the value of
a
+
b
a+b
a
+
b
is:
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