Question

Расставить пределы интегрирования.

Answer 1

$x^2+y^2=2x; ,; ; x+z=2; ,; ; zgeq 0; .\\x^2-2x+y^2=0; ,; ; (x-1)^2+y^2=1; ,\\y^2=1-(x-1)^2; ,; ; y=pm sqrt{1-(x-1)^2}\\iiint limits _{V}f(x,y,z)dx, dy, dz=iint limits _{D}dx, dyint limits_{0}^{2-x}f(x,y)dz=\\=int limits _{0}^2dx;int limits _{-sqrt{1-(x-1)^2}}^{sqrt{1-(x-1)^2}}dyint limits _{0}^{2-x}dz=int limits _{0}^2dx; intlimits^{sqrt{2x-x^2}}_{-sqrt{2x-x^2}}, dy intlimits^{2-x}_0, dz$