Question Number 184869 by yaslm last updated on 13/Jan/23
Answered by mr W last updated on 20/Jan/23
Commented by mr W last updated on 20/Jan/23
$${y}=\left(\frac{{x}}{{b}}\right)^{{n}} {h} \\ $$$${A}=\int_{\mathrm{0}} ^{{b}} \left(\frac{{x}}{{b}}\right)^{{n}} {hdx}=\frac{{b}^{{n}+\mathrm{1}} {h}}{\left({n}+\mathrm{1}\right){b}^{{n}} }=\frac{{bh}}{{n}+\mathrm{1}}\:\checkmark \\ $$$$\left({b}−{X}\right){A}=\int_{\mathrm{0}} ^{{b}} {x}\left(\frac{{x}}{{b}}\right)^{{n}} {hdx}=\frac{{b}^{{n}+\mathrm{2}} {h}}{\left({n}+\mathrm{2}\right){b}^{{n}} }=\frac{{b}^{\mathrm{2}} {h}}{{n}+\mathrm{2}} \\ $$$$\left({b}−{X}\right)\frac{{bh}}{{b}+\mathrm{1}}=\frac{{b}^{\mathrm{2}} {h}}{{n}+\mathrm{2}} \\ $$$${b}−{X}=\frac{\left({n}+\mathrm{1}\right){b}}{{n}+\mathrm{2}} \\ $$$$\Rightarrow{X}=\frac{{b}}{{n}+\mathrm{2}}\:\checkmark \\ $$