Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Calculus of Variations Conditions for Extrema
What is the extremal of the functional
\(\displaystyle J[y]=\int_{-1}^0\left(12 x y-\left(y^{\prime}\right)^2\right) d x\)
subject to y(0) = 0 and y(-1) = 1?
1
y = x2
2
\(y=\frac{2 x^2+x^4}{3}\)
3
y = -x3
4
\(y=\frac{x^2+x^4}{2}\)
5
Question Not Attempted