4.28 Variation Calculus

Condition: Find the extreme functionality and explore it using the 2nd order conditions. \ [\ begin {array} {l} \ int_ {0}^{\ frac {\ pi}}} \ left (\ dot {x} {2} -x^{2} +4 x {SH} T \ RIGHT) D T \ RIGHTARROW \ MATHRM {Extr} \\ X (0) = x \ Left (\ frac {\ pi} {2} \ right) = 0 \ End {Array} \]]