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Mathematics
Mathematics
Problem
For a continuous function
f
f
f
, the net signed area between the graph of
f
f
f
and the
t
t
t
-axis from
t
=
1
t=1
t
=
1
to
t
=
4
t=4
t
=
4
is
6
6
6
square units, and the net signed area from
t
=
4
t=4
t
=
4
to
t
=
7
t=7
t
=
7
is
−
3
-3
−
3
square units. If
F
(
x
)
=
∫
1
x
f
(
t
)
d
t
F(x)=\displaystyle\int_{1}^{x} f(t)\,dt
F
(
x
)
=
∫
1
x
f
(
t
)
d
t
and
F
(
1
)
=
2
F(1)=2
F
(
1
)
=
2
, determine
F
(
7
)
F(7)
F
(
7
)
.
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