柱坐標(biāo),z的變化范圍是√(x²+y²)1] rz/(r²+1) |[r---->1] dr
=2π∫[0--->1] r(1-r)/(r²+1) dr
=2π∫[0--->1] (r-r²)/(r²+1) dr
=2π∫[0--->1] (r-r²-1+1)/(r²+1) dr
=2π∫[0--->1] r/(r²+1) dr-2π∫[0--->1] 1 dr+2π∫[0--->1] 1/(r²+1) dr
=π∫[0--->1] 1/(r²+1) d(r²)-2π+2πarctanr
=πl(wèi)n(r²+1)-2π+2πarctanr |[0--->1]
=πl(wèi)n2-2π+π²/2