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Mathematics
Mathematics
Problem
A continuous function
g
g
g
satisfies
g
(
x
)
≥
0
g(x)\ge 0
g
(
x
)
≥
0
on
[
0
,
3
]
[0,3]
[
0
,
3
]
and
g
(
x
)
≤
0
g(x)\le 0
g
(
x
)
≤
0
on
[
3
,
6
]
[3,6]
[
3
,
6
]
. The area of the region between the graph of
g
g
g
and the
x
x
x
-axis is
4
4
4
square units on
[
0
,
3
]
[0,3]
[
0
,
3
]
and
6
6
6
square units on
[
3
,
6
]
[3,6]
[
3
,
6
]
. Find the value of
∫
0
6
g
(
x
)
d
x
\displaystyle\int_{0}^{6} g(x)\,dx
∫
0
6
g
(
x
)
d
x
.
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