Hello! I need help with a problem I cant solve no matter what I try. Its given to calculate
Double Integral(x^2+y^2)dxdy on area given with equations x^2-y^2=1,4 and xy=1,3 in the first quadrant. There is a hint to use u=xy and v=x^2-y^2 and I don't know how to get the Jacobian to be an actual value not dependent on x or y
#double integrals and jacobian
quiet turret
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Hello! I need help with a problem I cant solve no matter what I try. Its given t...
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spark rock
Hello! I need help with a problem I cant solve no matter what I try. Its given t...
the Jacobian doesnt have to be a number
like the Jacobian for polar coordinates is r, which isnt a number
quiet turret
Oh yeah but i mean wouldnt I get a Jacobian has x or y in it
spark rock
no
quiet turret
But i switch to integration with u v
spark rock
you have x=g(u,v) and y=h(u,v)
quiet turret
Yeah but with the substitution u=xy and v=x^2-y^2 im having trouble actually getting those functions
And valid results to partially derive
spark rock
$u=xy\to 1 = xy_u+yx_u$ and $v=x^2-y^2\to 0 = 2xx_u-2yy_u$
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Omegabet_
spark rock
which is a linear system in $x_u$ and $y_u$
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Omegabet_
spark rock
which are the things you want for the jacobian
quiet turret
Thank youb
, would it be too much to explain how you got the second part
Why is v becoming 0
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Omegabet_
quiet turret
Okay thank you, I will try to solve with this but may I ask for help if I get stuck 