<PRE><B>Question 859029</B>
First find the area.
{{{A=int(e^(-x),dx,0,1)=-e^(-x)+C=(e-1)/e=0.632}}}
Now,
{{{x[c]*A=int(xe^(-x),dx,0,1)}}}
{{{x[c]*A=-e^(-x)(x+1)+C}}}
{{{x[c]*A=(e-2)/e}}}
{{{x[c]*0.632=0.264}}}
{{{x[c]=0.418}}}
.
.
{{{y[c]*A=(1/2)*int((e^(-x))^2,dx,0,1)}}}
{{{y[c]*A=(1/2)*(-(1/2)(e^(-2x)))+C}}}
{{{y[c]*A=(1/4)((e^2-1)/e^2)}}}
{{{y[c]*0.632=0.216}}}
{{{y[c]=0.342}}}</PRE>