Let f:DtoR be defined as f(x,y,z)=xyz, where D=(x,y,z)inR^3/x^2+y^2+z^2<1. Let P denote the plane (x,y,z)/2x+3y+5z=0. Then intDcap Pf,dx,dy,dz is:

Q41Section II (Mathematics)41 of 190

An odd integrand over a centrally symmetric slice vanishes

Let $f:D\to\mathbb{R}$ be defined as $f(x,y,z)=xyz$ , where $D=\{(x,y,z)\in\mathbb{R}^3/x^2+y^2+z^2<1\}$ . Let P denote the plane $\{(x,y,z)/2x+3y+5z=0\}$ . Then $\int_{D\cap P}f\,dx\,dy\,dz$ is:

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