设D={(x,y)|x^2+y^2≤4},则∫∫x^2dxdy=?

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设D={(x,y)|x^2+y^2≤4},则∫∫x^2dxdy=?设D={(x,y)|x^2+y^2≤4},则∫∫x^2dxdy=?设D={(x,y)|x^2+y^2≤4},则∫∫x^2dxdy=?∵

设D={(x,y)|x^2+y^2≤4},则∫∫x^2dxdy=?
设D={(x,y)|x^2+y^2≤4},则∫∫x^2dxdy=?

设D={(x,y)|x^2+y^2≤4},则∫∫x^2dxdy=?
∵∫∫D x² dxdy = ∫∫D y² dxdy
∴∫∫D x² dxdy
= (1/2)∫∫D (x² + y²) dxdy
= (1/2)∫(0→2π) dθ ∫(0→2) r³ dr
= 1/2 * 2π * 1/4 * 2⁴
= 4π