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Unit Square Integral -- from Wolfram MathWorld

Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy =1/6[sqrt(2)+sinh^(-1)(1)], (1) which give the average distances in square point picking from a point picked at random in a unit square to a corner and to the center, respectively. Unit square integrals involving the absolute value are given by int_0^1int_0^1|x-y|^ndxdy = 2/((n+1)(n+2)) (2) int_0^1int_0^1|x+y|^ndxdy...



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Unit Square Integral -- from Wolfram MathWorld

https://mathworld.wolfram.com/UnitSquareIntegral.html

Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy =1/6[sqrt(2)+sinh^(-1)(1)], (1) which give the average distances in square point picking from a point picked at random in a unit square to a corner and to the center, respectively. Unit square integrals involving the absolute value are given by int_0^1int_0^1|x-y|^ndxdy = 2/((n+1)(n+2)) (2) int_0^1int_0^1|x+y|^ndxdy...



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https://mathworld.wolfram.com/UnitSquareIntegral.html

Unit Square Integral -- from Wolfram MathWorld

Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy =1/6[sqrt(2)+sinh^(-1)(1)], (1) which give the average distances in square point picking from a point picked at random in a unit square to a corner and to the center, respectively. Unit square integrals involving the absolute value are given by int_0^1int_0^1|x-y|^ndxdy = 2/((n+1)(n+2)) (2) int_0^1int_0^1|x+y|^ndxdy...

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      Unit Square Integral -- from Wolfram MathWorld
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      Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy =1/6[sqrt(2)+sinh^(-1)(1)], (1) which give the average distances in square point picking from a point picked at random in a unit square to a corner and to the center, respectively. Unit square integrals involving the absolute value are given by int_0^1int_0^1|x-y|^ndxdy = 2/((n+1)(n+2)) (2) int_0^1int_0^1|x+y|^ndxdy...
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      Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy =1/6[sqrt(2)+sinh^(-1)(1)], (1) which give the average distances in square point picking from a point picked at random in a unit square to a corner and to the center, respectively. Unit square integrals involving the absolute value are given by int_0^1int_0^1|x-y|^ndxdy = 2/((n+1)(n+2)) (2) int_0^1int_0^1|x+y|^ndxdy...

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      Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy =1/6[sqrt(2)+sinh^(-1)(1)], (1) which give the average distances in square point picking from a point picked at random in a unit square to a corner and to the center, respectively. Unit square integrals involving the absolute value are given by int_0^1int_0^1|x-y|^ndxdy = 2/((n+1)(n+2)) (2) int_0^1int_0^1|x+y|^ndxdy...

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      Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy =1/6[sqrt(2)+sinh^(-1)(1)], (1) which give the average distances in square point picking from a point picked at random in a unit square to a corner and to the center, respectively. Unit square integrals involving the absolute value are given by int_0^1int_0^1|x-y|^ndxdy = 2/((n+1)(n+2)) (2) int_0^1int_0^1|x+y|^ndxdy...
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