- #1

Hummingbird25

- 86

- 0

**Integral inequality and comparison**

## Homework Statement

Prove the inequality

[tex]\frac{2}{(n+1) \cdot \pi} \leq a_n \leq \frac{2}{n \pi}}[/tex]

where [tex]a_n = \int_{0}^{\pi} \frac{sin(x)}{n \cdot \pi +x} dx[/tex]

and [tex]n \geq 1[/tex]

## The Attempt at a Solution

Proof:

If n increased the left side of inequality because smaller every time it increases while the integral becomes larger, then by camparison the right side of the inequality always will become larger, than the integral.

Is this proof enough?

Sincerely

Maria.

Last edited: