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Mathematics
Problem
Let
A
=
∫
1
5
(
u
(
x
)
−
v
(
x
)
)
d
x
A=\displaystyle \int_{1}^{5}\bigl(u(x)-v(x)\bigr)\,dx
A
=
∫
1
5
(
u
(
x
)
−
v
(
x
)
)
d
x
. Without evaluating any integrals, determine the value of
∫
1
5
(
u
(
x
)
+
7
−
(
v
(
x
)
+
7
)
)
d
x
\displaystyle \int_{1}^{5}\bigl(u(x)+7-(v(x)+7)\bigr)\,dx
∫
1
5
(
u
(
x
)
+
7
−
(
v
(
x
)
+
7
)
)
d
x
in terms of
A
A
A
and briefly explain why your answer holds.
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