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Mathematics
Problem
Identify the correct property of indefinite integrals for the sum of two functions
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
. a)
∫
[
f
(
x
)
+
g
(
x
)
]
d
x
=
∫
f
(
x
)
d
x
⋅
∫
g
(
x
)
d
x
\displaystyle \int [f(x)+g(x)]\,dx = \int f(x)\,dx \cdot \int g(x)\,dx
∫
[
f
(
x
)
+
g
(
x
)]
d
x
=
∫
f
(
x
)
d
x
⋅
∫
g
(
x
)
d
x
b)
∫
[
f
(
x
)
+
g
(
x
)
]
d
x
=
∫
f
(
x
)
d
x
+
∫
g
(
x
)
d
x
\displaystyle \int [f(x)+g(x)]\,dx = \int f(x)\,dx + \int g(x)\,dx
∫
[
f
(
x
)
+
g
(
x
)]
d
x
=
∫
f
(
x
)
d
x
+
∫
g
(
x
)
d
x
c)
∫
[
f
(
x
)
+
g
(
x
)
]
d
x
=
∫
f
(
x
)
d
x
−
∫
g
(
x
)
d
x
\displaystyle \int [f(x)+g(x)]\,dx = \int f(x)\,dx - \int g(x)\,dx
∫
[
f
(
x
)
+
g
(
x
)]
d
x
=
∫
f
(
x
)
d
x
−
∫
g
(
x
)
d
x
d)
∫
[
f
(
x
)
+
g
(
x
)
]
d
x
=
∫
[
f
(
x
)
g
(
x
)
]
d
x
\displaystyle \int [f(x)+g(x)]\,dx = \int [f(x)g(x)]\,dx
∫
[
f
(
x
)
+
g
(
x
)]
d
x
=
∫
[
f
(
x
)
g
(
x
)]
d
x
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