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Mathematics
Mathematics
Problem
Given
∫
1
4
f
(
t
)
d
t
=
6
\displaystyle \int_{1}^{4} f(t)\,dt = 6
∫
1
4
f
(
t
)
d
t
=
6
and
∫
4
6
f
(
t
)
d
t
=
−
2
\displaystyle \int_{4}^{6} f(t)\,dt = -2
∫
4
6
f
(
t
)
d
t
=
−
2
, where
F
F
F
satisfies
F
′
(
x
)
=
f
(
x
)
F'(x)=f(x)
F
′
(
x
)
=
f
(
x
)
and
F
(
1
)
=
2
F(1)=2
F
(
1
)
=
2
, determine the value of
F
(
6
)
F(6)
F
(
6
)
.
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