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Mathematics
Mathematics
Problem
Let
f
f
f
and
g
g
g
be integrable on
[
−
3
,
4
]
[-3,4]
[
−
3
,
4
]
such that
∫
−
3
1
f
(
x
)
d
x
=
5
,
∫
1
4
f
(
x
)
d
x
=
−
2
,
∫
−
3
4
g
(
x
)
d
x
=
8
,
\displaystyle \int_{-3}^{1} f(x)\,dx = 5,\quad \int_{1}^{4} f(x)\,dx = -2,\quad \int_{-3}^{4} g(x)\,dx = 8,
∫
−
3
1
f
(
x
)
d
x
=
5
,
∫
1
4
f
(
x
)
d
x
=
−
2
,
∫
−
3
4
g
(
x
)
d
x
=
8
,
and
∫
1
4
[
f
(
x
)
+
g
(
x
)
]
d
x
=
1.
\displaystyle \int_{1}^{4} [f(x)+g(x)]\,dx = 1.
∫
1
4
[
f
(
x
)
+
g
(
x
)]
d
x
=
1.
Find the value of
∫
−
3
1
g
(
x
)
d
x
\displaystyle \int_{-3}^{1} g(x)\,dx
∫
−
3
1
g
(
x
)
d
x
. a)
11
11
11
b)
5
5
5
c)
−
5
-5
−
5
d)
3
3
3
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