二重积分∫∫√x²+y²dxdy D:x²+y²≤a²

2025-02-26 08:20:12
推荐回答(2个)
回答1:

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

回答2:

用极坐标行不?