Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Calculus of Variations Euler-lagrange Equation
Let x*(t) be the curve which minimizes the functional
\(J(x)=\int_0^1\left[x^2(t)+\dot{x}^2(t)\right] d t \)
satisfying x(0) = 0, x(1) = 1. Then the value of x* \(\left(\frac{1}{2}\right)\) is
1
\(\frac{\sqrt{e}}{1+e}\)
2
\(\frac{2 \sqrt{e}}{1+e}\)
3
\(\frac{\sqrt{e}}{1+2 e}\)
4
\(\frac{2 \sqrt{e}}{1+2 e}\)
5
Question Not Attempted