極坐標(biāo)求解
圍成區(qū)域z1在上z2在下
z1=√(x²+y²),z2=x²+y²
令z1=z2
√(x²+y²)=x²+y²
即r=r²
r=0,r=1
極坐標(biāo)下D在xoy平面投影可標(biāo)示為
0≤θ≤2π,0≤r≤1
體積
V=∫∫(D)(z1-z2)dv
=∫(0,2π)dθ∫(r-r²)rdr
=2π∫(r²-r^3)dr
=2π[(1/3)r^3-(1/4)r^4]|(0,1)
=π/6