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Mathematics
Problem
Statement I *The function
f
(
x
)
=
∫
0
x
1
+
t
2
d
t
f(x) = \int_{0}^{x} \sqrt{1+t^2} dt
f
(
x
)
=
∫
0
x
1
+
t
2
d
t
is an odd function and
g
(
x
)
=
f
′
(
x
)
g(x) = f'(x)
g
(
x
)
=
f
′
(
x
)
is an even function.* Statement II *For a differentiable function
f
(
x
)
f(x)
f
(
x
)
if
f
′
(
x
)
f'(x)
f
′
(
x
)
is an even function, then
f
(
x
)
f(x)
f
(
x
)
is an odd function.*
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