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Mathematics
Mathematics
Problem
For a real parameter
k
k
k
the following values are given:
∫
0
2
f
(
x
)
d
x
=
k
,
\displaystyle\int_{0}^{2} f(x)\,dx = k,
∫
0
2
f
(
x
)
d
x
=
k
,
∫
2
5
f
(
x
)
d
x
=
3
k
−
1
,
\displaystyle\int_{2}^{5} f(x)\,dx = 3k-1,
∫
2
5
f
(
x
)
d
x
=
3
k
−
1
,
∫
0
5
[
2
f
(
x
)
−
g
(
x
)
]
d
x
=
5
k
+
4.
\displaystyle\int_{0}^{5}[2f(x)-g(x)]\,dx = 5k+4.
∫
0
5
[
2
f
(
x
)
−
g
(
x
)]
d
x
=
5
k
+
4.
Determine
∫
0
5
g
(
x
)
d
x
\displaystyle\int_{0}^{5} g(x)\,dx
∫
0
5
g
(
x
)
d
x
in terms of
k
k
k
.
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