Another example of Jacobian
Evaluate
I
≡
⌠
⌡
1/2
0
⌠
⌡
1 −2
y
0
exp
⎛
⎝
x
x
+ 2
y
⎞
⎠
d
x
d
y
.
(1)
Hint:
Draw the integral area.
Change the variables from (
x
,
y
) to (
u
,
v
) by
u
=
x
,
v
=
x
+ 2
y
.
d
x
d
y
=
⎢
⎢
∂(
x
,
y
)
∂(
u
,
v
)
⎢
⎢
d
u
d
v
.
(2)
File translated from T
E
X by
T
T
H
, version 4.03.
On 15 Sep 2025, 14:20.