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Mathematics
Mathematics
Problem
For functions
f
f
f
and
g
g
g
, the following values are known:
∫
0
2
f
(
x
)
d
x
=
5
,
∫
2
5
f
(
x
)
d
x
=
−
2
,
∫
0
2
g
(
x
)
d
x
=
−
4
,
∫
2
5
g
(
x
)
d
x
=
1.
\displaystyle\int_{0}^{2} f(x)\,dx = 5,\quad \int_{2}^{5} f(x)\,dx = -2,\quad \int_{0}^{2} g(x)\,dx = -4,\quad \int_{2}^{5} g(x)\,dx = 1.
∫
0
2
f
(
x
)
d
x
=
5
,
∫
2
5
f
(
x
)
d
x
=
−
2
,
∫
0
2
g
(
x
)
d
x
=
−
4
,
∫
2
5
g
(
x
)
d
x
=
1.
Evaluate
∫
0
5
(
−
2
f
(
x
)
+
3
g
(
x
)
)
d
x
\displaystyle\int_{0}^{5}\bigl(-2f(x)+3g(x)\bigr)\,dx
∫
0
5
(
−
2
f
(
x
)
+
3
g
(
x
)
)
d
x
.
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