将直角坐标换为极坐标x=rcost,y=rsint那么∫∫√x²+y²dxdy D:x²+y²≤a² =∫∫r√(rcost)²+(rsint)²drdt D:0≤r≤a,0≤t≤2π=∫∫r*rdrdt=∫∫r²drdt=∫r²dr *∫dt D:0≤r≤a,0≤t≤2π=r³/3(从0到a)* t(从0到2π)=a³/3*2π=2πa³/3
用极坐标行不?