没有Fubini的多变量积分

JORGE ANGULO 06/21/2018. 1 answers, 34 views
real-analysis integration

我试图解决以下问题:

设$ K = \ {(x,y,z)\ in \ mathbb {R} ^ {3}:| x | + | y | \ leq 1,\ z \ geq 0,\ x ^ 2 + y ^ 2 + z ^ 2 \ leq 1 \} $

在不使用Fubini定理的情况下显示$ \ int_K xz ^ 2 dxdydz = 0 $。

除了可视化域名之外,我根本不知道从哪里开始,这似乎没有帮助。

我想知道如何解决这个问题。

1 Answers


Ben McKay 06/21/2018.

通过$ X = -x $更改变量,以确保您获得与相反符号相同的积分。 通常,在保持域的变换的体积下其符号改变的函数的积分为零。


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