It is proved that f (x, y) = sin (XY) / √ (x ^ 2 + y ^ 2) when x ^ 2 + y ^ 2 ≠ 0, and f (x, y) = 0 is continuous at (0,0) when x ^ 2 + y ^ 2 = 0

It is proved that f (x, y) = sin (XY) / √ (x ^ 2 + y ^ 2) when x ^ 2 + y ^ 2 ≠ 0, and f (x, y) = 0 is continuous at (0,0) when x ^ 2 + y ^ 2 = 0

Note: F (x, y) DXDY is actually a constant, let a = ∫∫ f (x, y) DXDY, then f (x, y) = [1 - (x ^ 2 + y ^ 2)] ^ 0.5 - π A / 8 do double integration on both sides, then: ∫∫ f (x, y) DXDY integral region is: X & # 178; + (Y-1 / 2) & # 178; ≤ 1 / 4, X ≥ 0, polar coordinate equation of circle is: r = sin θ, θ: 0 - >