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Mathematics
Problem
Which of the following correctly expresses
∫
a
b
(
5
f
(
x
)
−
2
g
(
x
)
)
d
x
\displaystyle\int_a^b \bigl(5f(x)-2g(x)\bigr)\,dx
∫
a
b
(
5
f
(
x
)
−
2
g
(
x
)
)
d
x
in terms of separate integrals of
f
f
f
and
g
g
g
? a)
5
∫
b
a
f
(
x
)
d
x
−
2
∫
b
a
g
(
x
)
d
x
5\displaystyle\int_b^a f(x)\,dx - 2\displaystyle\int_b^a g(x)\,dx
5
∫
b
a
f
(
x
)
d
x
−
2
∫
b
a
g
(
x
)
d
x
b)
∫
a
b
f
(
x
)
d
x
+
∫
a
b
g
(
x
)
d
x
\displaystyle\int_a^b f(x)\,dx + \displaystyle\int_a^b g(x)\,dx
∫
a
b
f
(
x
)
d
x
+
∫
a
b
g
(
x
)
d
x
c)
5
∫
a
b
f
(
x
)
d
x
−
2
∫
a
b
g
(
x
)
d
x
5\displaystyle\int_a^b f(x)\,dx - 2\displaystyle\int_a^b g(x)\,dx
5
∫
a
b
f
(
x
)
d
x
−
2
∫
a
b
g
(
x
)
d
x
d)
1
5
∫
a
b
f
(
x
)
d
x
−
1
2
∫
a
b
g
(
x
)
d
x
\tfrac15\displaystyle\int_a^b f(x)\,dx - \tfrac12\displaystyle\int_a^b g(x)\,dx
5
1
∫
a
b
f
(
x
)
d
x
−
2
1
∫
a
b
g
(
x
)
d
x
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