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Mathematics
Problem
Let
g
g
g
be a continuous function and let
F
F
F
satisfy
d
F
d
x
=
g
(
x
)
\dfrac{dF}{dx}=g(x)
d
x
d
F
=
g
(
x
)
with the initial condition
F
(
1
)
=
3
F(1)=3
F
(
1
)
=
3
. Which of the following expressions represents
F
(
x
)
F(x)
F
(
x
)
for all
x
x
x
in the domain of
g
g
g
? a)
3
+
∫
x
1
g
(
t
)
d
t
3+\displaystyle\int_{x}^{1} g(t)\,dt
3
+
∫
x
1
g
(
t
)
d
t
b)
∫
1
x
g
(
t
)
d
t
\displaystyle\int_{1}^{x} g(t)\,dt
∫
1
x
g
(
t
)
d
t
c)
3
+
∫
1
x
g
(
t
)
d
t
3+\displaystyle\int_{1}^{x} g(t)\,dt
3
+
∫
1
x
g
(
t
)
d
t
d)
3
+
g
(
x
)
(
x
−
1
)
3+g(x)(x-1)
3
+
g
(
x
)
(
x
−
1
)
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