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Mathematics
Problem
Which of the following identities is always true for any integrable function
f
f
f
and real constant
c
c
c
? a)
∫
a
b
c
f
(
x
)
d
x
=
1
c
∫
a
b
f
(
x
)
d
x
\displaystyle \int_a^b c\,f(x)\,dx = \tfrac{1}{c}\int_a^b f(x)\,dx
∫
a
b
c
f
(
x
)
d
x
=
c
1
∫
a
b
f
(
x
)
d
x
b)
∫
a
b
c
f
(
x
)
d
x
=
c
∫
a
b
f
(
x
)
d
x
\displaystyle \int_a^b c\,f(x)\,dx = c\int_a^b f(x)\,dx
∫
a
b
c
f
(
x
)
d
x
=
c
∫
a
b
f
(
x
)
d
x
c)
∫
a
b
c
f
(
x
)
d
x
=
∫
c
a
c
b
f
(
x
)
d
x
\displaystyle \int_a^b c\,f(x)\,dx = \int_{ca}^{cb} f(x)\,dx
∫
a
b
c
f
(
x
)
d
x
=
∫
c
a
c
b
f
(
x
)
d
x
d)
∫
a
b
c
f
(
x
)
d
x
=
c
∫
b
a
f
(
x
)
d
x
\displaystyle \int_a^b c\,f(x)\,dx = c\int_b^a f(x)\,dx
∫
a
b
c
f
(
x
)
d
x
=
c
∫
b
a
f
(
x
)
d
x
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