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Mathematics
Mathematics
Problem
Let
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
be a continuous function given by
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
f(x+y) = f(x) + f(y)
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
for all
x
,
y
∈
R
x, y \in \mathbb{R}
x
,
y
∈
R
. If
∫
0
2
f
(
x
)
d
x
=
α
\int_0^2 f(x) dx = \alpha
∫
0
2
f
(
x
)
d
x
=
α
, then
∫
−
2
2
f
(
x
)
d
x
\int_{-2}^2 f(x) dx
∫
−
2
2
f
(
x
)
d
x
is equal to a.
2
α
2\alpha
2
α
b.
α
\alpha
α
c. 0 d. None of these
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