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Calculate the integral $int_Bfracx^3y^3dlambda_2$ over $B=[(x,y): x^2

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0

$begingroup$

$$int_Bfracx^3y^3dlambda_2,$$ where $$B=(x,y): x^2<8y<8x^2; y^2<x<8y^2$$ This is the first time for me, where $2$ variables depend on each other in this manner. I wanted to do some smart substitution, but can't figure out one. Any help appreciated. I also drew this area, but it does not much easier, since it is a bit irregular shape. What is the method in this type of situations?

real-analysis integration analysis lebesgue-integral

share|cite|improve this question

edited Mar 29 at 22:32

MarianD

2,2181618

asked Mar 29 at 21:48

ryszard egginkryszard eggink

415110

$endgroup$

add a comment | 

0

$begingroup$

$$int_Bfracx^3y^3dlambda_2,$$ where $$B=(x,y): x^2<8y<8x^2; y^2<x<8y^2$$ This is the first time for me, where $2$ variables depend on each other in this manner. I wanted to do some smart substitution, but can't figure out one. Any help appreciated. I also drew this area, but it does not much easier, since it is a bit irregular shape. What is the method in this type of situations?

real-analysis integration analysis lebesgue-integral

share|cite|improve this question

edited Mar 29 at 22:32

MarianD

2,2181618

asked Mar 29 at 21:48

ryszard egginkryszard eggink

415110

$endgroup$

add a comment | 

$begingroup$

$$int_Bfracx^3y^3dlambda_2,$$ where $$B=(x,y): x^2<8y<8x^2; y^2<x<8y^2$$ This is the first time for me, where $2$ variables depend on each other in this manner. I wanted to do some smart substitution, but can't figure out one. Any help appreciated. I also drew this area, but it does not much easier, since it is a bit irregular shape. What is the method in this type of situations?

real-analysis integration analysis lebesgue-integral

share|cite|improve this question

edited Mar 29 at 22:32

MarianD

2,2181618

asked Mar 29 at 21:48

ryszard egginkryszard eggink

415110

$endgroup$

share|cite|improve this question

edited Mar 29 at 22:32

MarianD

2,2181618

asked Mar 29 at 21:48

ryszard egginkryszard eggink

415110

share|cite|improve this question

edited Mar 29 at 22:32

MarianD

2,2181618

asked Mar 29 at 21:48

ryszard egginkryszard eggink

415110

edited Mar 29 at 22:32

MarianD

2,2181618

edited Mar 29 at 22:32

MarianD

2,2181618

asked Mar 29 at 21:48

ryszard egginkryszard eggink

415110

asked Mar 29 at 21:48

ryszard egginkryszard eggink

415110