设 $D=\left\{(x,y)|x+y≤1,x≥0,y≥0\right\}$,令 $I= \iint _{D} \sqrt {x^{2}+y^{2}}dxdy$,$J= \iint _{D} \ln (1+x^{2}+y^{2})dxdy$,$K= \iint _{D}(x^{2}+y^{2})dxdy$, 则
$\text{A.}$ $I < J < K$
$\text{B.}$ $J < K < I$
$\text{C.}$ $J < I < K$
$\text{D.}$ $K < J < I$