Question Number 195838 by sonukgindia last updated on 11/Aug/23
Answered by sniper237 last updated on 11/Aug/23
$${Area}=\int_{{u}} ^{{v}} {f}\left({x}\right){dx}\overset{{t}={lnx}} {=}\int_{{a}} ^{{b}} \:\frac{{dt}}{\:\sqrt{\left({t}−{a}\right)\left({b}−{t}\right)}}\: \\ $$$$\:\:\:\overset{{s}=\frac{{a}+{b}}{\mathrm{2}}−{t}} {=}\int_{−{c}} ^{{c}} \frac{{ds}}{\:\sqrt{{c}^{\mathrm{2}} −{s}^{\mathrm{2}} }}\:\overset{{s}={c}\:\:{sin}\theta} {=}\:\mathrm{2}\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \:{d}\theta\:=\pi \\ $$