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Mathematics
Mathematics
Problem
Let
f
f
f
be continuous on
[
0
,
5
]
[0,5]
[
0
,
5
]
. Given
∫
0
5
f
(
x
)
d
x
=
12
\displaystyle \int_{0}^{5} f(x)\,dx = 12
∫
0
5
f
(
x
)
d
x
=
12
and
∫
0
5
(
2
x
−
1
)
f
(
x
)
d
x
=
3
\displaystyle \int_{0}^{5} \bigl(2x-1\bigr) f(x)\,dx = 3
∫
0
5
(
2
x
−
1
)
f
(
x
)
d
x
=
3
, find
∫
0
5
x
f
(
x
)
d
x
\displaystyle \int_{0}^{5} x f(x)\,dx
∫
0
5
x
f
(
x
)
d
x
. a)
9
2
\dfrac{9}{2}
2
9
b)
15
2
\dfrac{15}{2}
2
15
c)
4
4
4
d)
5
2
\dfrac{5}{2}
2
5
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