Show that $lim\int_{-n}^n f=\int_{\mathbb{R}} f$

Question

I need help showing that that $lim\int_{-n}^n f=\int_{\mathbb{R}} f$ where $f$ is a nonegative measurable function. For the case that $f$ is integrable over ${\mathbb{R}}$ I think I solved using Lebesgue Dominated convergence Theorem on the sequence $f_n=f\chi_{[-n,n]}$. I have no idea how to proceed with the case $\int_{\mathbb{R}} f=\infty$

Any help would be greatly appreciated

Answer 1

Hint: Try the monotone convergence theorem.