Let J(u) = \(\rm \int_0^1\left[u_x^2+4 \frac{u^2}{x^2}\right] x\ d x\), where u(x) is a smooth function defined on [0, 1] satisfying u(0) = 0 and u(1) = 1. Which of the function minimizes J?
1
u(x) = x2
2
\(\rm u(x)=\frac{1}{\sqrt{2}} x^2\)
3
\(\rm u(x)=\frac{1}{2} x^2\)
4
\(\rm u(x)=\frac{1}{4} x^2\)
5
Question Not Attempted