如图第五题,三重积分,跪求大神指点一二,要过程呦

2025-04-29 05:53:52
推荐回答(1个)
回答1:

∫[2ln(x^2 + y^2 + z^2 + 1) / (x^2 + y^2 + z^2 + 1)]dv
= ∫2ln(x^2 + y^2 + z^2 + 1) d[ln(x^2 + y^2 + z^2 + 1)]
= [ln(x^2 + y^2 + z^2 + 1)]^2 + C
在球面中,有x^2、y^2、z^2∈[0,1]
I = 4(ln2)^2