- #1

- 214

- 0

## Homework Statement

Given the integral f(t)=sin(1/t)dt from 1/pi to infinity. Examine if it is convergent.

## Homework Equations

No particular equation. But I know that if the integral of a function g is convergent and there's another function h such that |h|<=g than the integral of h is also convergent.

## The Attempt at a Solution

What I tried so far is to take the Taylor serie T(X) of sin(x). Which is T(x)=x+o(x) where o(x) is a term that is negative if x is small enough. So I can estimate the function f(t): sin(1/t)>=1/t for large t.

But now I'm not really sure if I conclude the right thing out of this:

Does it follow, that because |sin(1/t)|>=1/t for large t and the integral of 1/t from 1/pi to infinity is not convergent, so sin(1/t) isn't convergent, too?

Or how can I solve this without using the Taylor serie? I think it isn't the right way.

Last edited: