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Mathematics
Problem
For the integral
I
=
∫
1
4
(
5
−
x
)
3
d
x
I=\int_{1}^{4}(5-x)^{3}\,dx
I
=
∫
1
4
(
5
−
x
)
3
d
x
, one performs the substitution
u
=
5
−
x
u=5-x
u
=
5
−
x
. Which of the following expressions is algebraically equivalent to
I
I
I
after the change of variable? a)
∫
4
1
u
3
d
u
\displaystyle\int_{4}^{1}u^{3}\,du
∫
4
1
u
3
d
u
b)
∫
1
4
(
5
−
u
)
3
d
u
\displaystyle\int_{1}^{4}(5-u)^{3}\,du
∫
1
4
(
5
−
u
)
3
d
u
c)
∫
1
4
u
3
d
u
\displaystyle\int_{1}^{4}u^{3}\,du
∫
1
4
u
3
d
u
d)
∫
1
4
(
−
1
)
u
3
d
u
\displaystyle\int_{1}^{4}(-1)\,u^{3}\,du
∫
1
4
(
−
1
)
u
3
d
u
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