# low convergence in \$ L ^ 2 \$ and integral convergence involving test functions

Let $$Omega$$ to be a bounded set of $$mathbb {R} ^ n$$ and $$(f_n) _n subset L ^ 2 ( Omega)$$ such as $$f_n to f in L ^ 2 ( Omega)$$ weakly $$L ^ 2 ( Omega)$$. Then for a given test function $$phi in C ^ infty_c ( Omega)$$, do we have the following convergent property:
$$int_ Omega | u_n | phi , dx to int_ Omega | u | phi , dx, quad textrm {as n to infty .}$$