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Mathematics
Problem
Let
F
(
x
)
=
∫
2
x
g
(
t
)
d
t
F(x)=\int_{2}^{x} g(t)\,dt
F
(
x
)
=
∫
2
x
g
(
t
)
d
t
, where
g
g
g
is continuous on its domain. Which of the following is equal to
F
′
(
x
)
F'(x)
F
′
(
x
)
for all
x
x
x
in the domain of
g
g
g
? a)
1
x
−
2
∫
2
x
g
(
t
)
d
t
\displaystyle \frac{1}{x-2}\int_{2}^{x} g(t)\,dt
x
−
2
1
∫
2
x
g
(
t
)
d
t
b)
g
(
2
)
g(2)
g
(
2
)
c)
g
(
x
)
g(x)
g
(
x
)
d)
∫
2
x
g
′
(
t
)
d
t
\displaystyle \int_{2}^{x} g'(t)\,dt
∫
2
x
g
′
(
t
)
d
t
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