variable change double integral region defined
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I am looking to solve this
$$int xy(x^2+y^2) dx dy$$
over the region region
$R:-3le x^2-y^2 le3, 1le xy le4$
I tried to change the coordinate system from $x$,$y$ to $u$,$v$
with $x^2-y^2=u$ and $xy=v$
$R:-3le u le3, 1le v le4$
but i am unable to express integrand $xy(x^2+y^2)$ especially $x^2+y^2$ in terms of $u$,$v$
I think I am working with the wrong substitution. Can someone suggest a better one?
integration multivariable-calculus change-of-variable
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up vote
0
down vote
favorite
I am looking to solve this
$$int xy(x^2+y^2) dx dy$$
over the region region
$R:-3le x^2-y^2 le3, 1le xy le4$
I tried to change the coordinate system from $x$,$y$ to $u$,$v$
with $x^2-y^2=u$ and $xy=v$
$R:-3le u le3, 1le v le4$
but i am unable to express integrand $xy(x^2+y^2)$ especially $x^2+y^2$ in terms of $u$,$v$
I think I am working with the wrong substitution. Can someone suggest a better one?
integration multivariable-calculus change-of-variable
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am looking to solve this
$$int xy(x^2+y^2) dx dy$$
over the region region
$R:-3le x^2-y^2 le3, 1le xy le4$
I tried to change the coordinate system from $x$,$y$ to $u$,$v$
with $x^2-y^2=u$ and $xy=v$
$R:-3le u le3, 1le v le4$
but i am unable to express integrand $xy(x^2+y^2)$ especially $x^2+y^2$ in terms of $u$,$v$
I think I am working with the wrong substitution. Can someone suggest a better one?
integration multivariable-calculus change-of-variable
I am looking to solve this
$$int xy(x^2+y^2) dx dy$$
over the region region
$R:-3le x^2-y^2 le3, 1le xy le4$
I tried to change the coordinate system from $x$,$y$ to $u$,$v$
with $x^2-y^2=u$ and $xy=v$
$R:-3le u le3, 1le v le4$
but i am unable to express integrand $xy(x^2+y^2)$ especially $x^2+y^2$ in terms of $u$,$v$
I think I am working with the wrong substitution. Can someone suggest a better one?
integration multivariable-calculus change-of-variable
integration multivariable-calculus change-of-variable
edited Sep 5 at 11:58
Deepesh Meena
3,8912825
3,8912825
asked Sep 5 at 11:50
Omen
13
13
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