Given that x0 1 find x on the interval 0 LE t LE T such tha

Given that x(0) = 1, find x(.) on the interval 0 LE t LE T such that J = T integrate 0 x^2 + x^2 dt is minimized.

Solution

We have to find J such that J is minimum

Use derivative test

J\'(T) = x(dot)²+T² ( by fundamental theorem)

J\"(T) = 2T >0 as T>0

Set J\'(T) to 0

T = square root of -X dot square