Question Number 153764 by mathdanisur last updated on 10/Sep/21
$$\mathrm{Prove}\:\mathrm{without}\:\mathrm{any}\:\mathrm{software}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\sqrt{\mathrm{1}\:-\:\left(\frac{\mathrm{x}\:+\:\mathrm{y}}{\mathrm{2}}\right)^{\mathrm{2}} }\:\mathrm{dxdy}\:>\:\frac{\pi}{\mathrm{4}} \\ $$
Commented by alisiao last updated on 10/Sep/21
$$\boldsymbol{{i}}\:\boldsymbol{{think}}\:\boldsymbol{{the}}\:\boldsymbol{{result}}\:=\:\frac{\boldsymbol{\pi}}{\mathrm{2}}\:\boldsymbol{{so}}\:,\:\frac{\boldsymbol{\pi}}{\mathrm{2}}>\frac{\boldsymbol{\pi}}{\mathrm{4}} \\ $$
Commented by mathdanisur last updated on 10/Sep/21
$$\mathrm{Ser},\:\:=\:\:\frac{\pi}{\mathrm{4}}\:\centerdot\:\frac{\pi}{\mathrm{4}}\:>\:\frac{\pi}{\mathrm{4}} \\ $$
Answered by alisiao last updated on 10/Sep/21
