Find the Jacobians ∂ x , y / ∂ u , v of the given transformations from variables x , y to variables u , v In the integral I = ∫ 0 ∞ ∫ 0 ∞ x 2 + y 2 1 + x 2 − y 2 2 e − 2 x y d x d y make the change of variables u = x 2 − y 2 v = 2 x y and evaluate I. Hint: Use (4.8) and the accompanying discussion.
Find the Jacobians ∂ x , y / ∂ u , v of the given transformations from variables x , y to variables u , v In the integral I = ∫ 0 ∞ ∫ 0 ∞ x 2 + y 2 1 + x 2 − y 2 2 e − 2 x y d x d y make the change of variables u = x 2 − y 2 v = 2 x y and evaluate I. Hint: Use (4.8) and the accompanying discussion.
Find the Jacobians
∂
x
,
y
/
∂
u
,
v
of the given transformations from variables
x
,
y
to variables
u
,
v
In the integral
I
=
∫
0
∞
∫
0
∞
x
2
+
y
2
1
+
x
2
−
y
2
2
e
−
2
x
y
d
x
d
y
make the change of variables
u
=
x
2
−
y
2
v
=
2
x
y
and evaluate I. Hint: Use (4.8) and the accompanying discussion.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Differential Equations: An Introduction to Modern Methods and Applications
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