Compute $iint sqrt frac 1-x^2-y^21+x^2+y^2,mathrm dxmathrm dy $

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Compute $$iint sqrt frac 1-x^2-y^21+x^2+y^2,mathrm dxmathrm dy $$ and $x^2+y^2leq 1$



I used polar coordinates then $sqrt dfrac 1-r^21+r^2r,mathrm drmathrm dtheta$, but couldn't continue.



Thanks for helping




calculus integration analysis




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    $$int_0^1 sqrtfrac1-r^21+r^2,r,dr=frac12int_0^1 sqrtfrac1-u1+u,du$$
    – Mark Viola
    Aug 7 at 16:08










  • how can i proof this inequality@MarkViola
    – user582369
    Aug 7 at 16:11











  • Well, it is an Equality, not an inequality. Substitute $u=r^2$.
    – Mark Viola
    Aug 7 at 16:12










  • tthanks for help @MarkViola
    – user582369
    Aug 7 at 16:20










  • You're welcome.
    – Mark Viola
    Aug 7 at 16:20














up vote
0
down vote

favorite
1












Compute $$iint sqrt frac 1-x^2-y^21+x^2+y^2,mathrm dxmathrm dy $$ and $x^2+y^2leq 1$



I used polar coordinates then $sqrt dfrac 1-r^21+r^2r,mathrm drmathrm dtheta$, but couldn't continue.



Thanks for helping




calculus integration analysis




share|cite|improve this question

















  • 1




    $$int_0^1 sqrtfrac1-r^21+r^2,r,dr=frac12int_0^1 sqrtfrac1-u1+u,du$$
    – Mark Viola
    Aug 7 at 16:08










  • how can i proof this inequality@MarkViola
    – user582369
    Aug 7 at 16:11











  • Well, it is an Equality, not an inequality. Substitute $u=r^2$.
    – Mark Viola
    Aug 7 at 16:12










  • tthanks for help @MarkViola
    – user582369
    Aug 7 at 16:20










  • You're welcome.
    – Mark Viola
    Aug 7 at 16:20












up vote
0
down vote

favorite
1









up vote
0
down vote

favorite
1






1





Compute $$iint sqrt frac 1-x^2-y^21+x^2+y^2,mathrm dxmathrm dy $$ and $x^2+y^2leq 1$



I used polar coordinates then $sqrt dfrac 1-r^21+r^2r,mathrm drmathrm dtheta$, but couldn't continue.



Thanks for helping




calculus integration analysis




share|cite|improve this question













Compute $$iint sqrt frac 1-x^2-y^21+x^2+y^2,mathrm dxmathrm dy $$ and $x^2+y^2leq 1$



I used polar coordinates then $sqrt dfrac 1-r^21+r^2r,mathrm drmathrm dtheta$, but couldn't continue.



Thanks for helping





calculus integration analysis





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 7 at 17:01









an4s

2,0382417




2,0382417









asked Aug 7 at 16:05









user582369

62




62







  • 1




    $$int_0^1 sqrtfrac1-r^21+r^2,r,dr=frac12int_0^1 sqrtfrac1-u1+u,du$$
    – Mark Viola
    Aug 7 at 16:08










  • how can i proof this inequality@MarkViola
    – user582369
    Aug 7 at 16:11











  • Well, it is an Equality, not an inequality. Substitute $u=r^2$.
    – Mark Viola
    Aug 7 at 16:12










  • tthanks for help @MarkViola
    – user582369
    Aug 7 at 16:20










  • You're welcome.
    – Mark Viola
    Aug 7 at 16:20












  • 1




    $$int_0^1 sqrtfrac1-r^21+r^2,r,dr=frac12int_0^1 sqrtfrac1-u1+u,du$$
    – Mark Viola
    Aug 7 at 16:08










  • how can i proof this inequality@MarkViola
    – user582369
    Aug 7 at 16:11











  • Well, it is an Equality, not an inequality. Substitute $u=r^2$.
    – Mark Viola
    Aug 7 at 16:12










  • tthanks for help @MarkViola
    – user582369
    Aug 7 at 16:20










  • You're welcome.
    – Mark Viola
    Aug 7 at 16:20







1




1




$$int_0^1 sqrtfrac1-r^21+r^2,r,dr=frac12int_0^1 sqrtfrac1-u1+u,du$$
– Mark Viola
Aug 7 at 16:08




$$int_0^1 sqrtfrac1-r^21+r^2,r,dr=frac12int_0^1 sqrtfrac1-u1+u,du$$
– Mark Viola
Aug 7 at 16:08












how can i proof this inequality@MarkViola
– user582369
Aug 7 at 16:11





how can i proof this inequality@MarkViola
– user582369
Aug 7 at 16:11













Well, it is an Equality, not an inequality. Substitute $u=r^2$.
– Mark Viola
Aug 7 at 16:12




Well, it is an Equality, not an inequality. Substitute $u=r^2$.
– Mark Viola
Aug 7 at 16:12












tthanks for help @MarkViola
– user582369
Aug 7 at 16:20




tthanks for help @MarkViola
– user582369
Aug 7 at 16:20












You're welcome.
– Mark Viola
Aug 7 at 16:20




You're welcome.
– Mark Viola
Aug 7 at 16:20















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