Integrate
∫
R
(
x
+
y
)
d
A
\displaystyle \int_{{R}}{\left({x}+{y}\right)}\ {d}{A}
∫
R
(
x
+
y
)
d
A
. Sketch the given region R and then the new region in the uv plane. R is bounded by
0
≤
x
≤
5
,
x
≤
y
≤
x
+
10
\displaystyle {0}\le{x}\le{5},{x}\le{y}\le{x}+{10}
0
≤
x
≤
5
,
x
≤
y
≤
x
+
10
.
Let
x
=
5
u
and
y
=
10
v
+
5
u
\displaystyle {x}={5}{u}{\quad\text{and}\quad}{y}={10}{v}+{5}{u}
x
=
5
u
and
y
=
10
v
+
5
u
.
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