Proving Monotonicity in the Dominated Convergence Theorem

[acazosa]

1. Homework Statement

So i have to solve this integral with dominate convergence theorem. How can i prove that the sequence f_{n}
it s monotone?

\lim_{n \rightarrow +infty} \int_{0}^{+infty} \frac{1 -sin(\frac{x}{n})}{\sqrt(x^2 +\frac{1}{2}}

 

[hunt_mat]

For $$0\leqslant x\leqslant\pi /2$$ then it boils down to showing that $$\sin (x/n)$$ is monotone which is easy right?

 

[acazosa]

sin(x/n) it s monotone just on some interval...I m sure that f_{n} it s not monotone jou can easily see that on wolframalpha, i m just guessing how to solve the integral with monotone convergence theorem.