Question $8$

Find the extremal $($if it exists$)$ of the isoperimetric problem with the functional

$I[x]={\displaystyle \underset{0}{\overset{2}{}}}(x^2-t^2)dt,$

subject to the conditions

${\displaystyle \underset{0}{\overset{2}{}}}xdt=1,x(0)=0,x(2)=2.$