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Mathematics
Mathematics
Problem
Given
g
(
x
)
=
∫
1
x
f
(
t
)
d
t
g(x)=\displaystyle\int_{1}^{x} f(t)\,dt
g
(
x
)
=
∫
1
x
f
(
t
)
d
t
, where
f
f
f
is continuous, which of the following is equal to
g
′
(
x
)
g'(x)
g
′
(
x
)
? a)
∫
1
x
f
′
(
t
)
d
t
\displaystyle\int_{1}^{x} f'(t)\,dt
∫
1
x
f
′
(
t
)
d
t
b)
f
(
x
)
f(x)
f
(
x
)
c)
f
′
(
x
)
f'(x)
f
′
(
x
)
d)
f
(
x
)
−
f
(
1
)
f(x)-f(1)
f
(
x
)
−
f
(
1
)
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