How to show that $ int_0^1frac{sin(frac{1}{x})}{x^2}dx$ diverges?

Question

I'm trying to prove that the following integral diverges:
$$
int_0^1frac{sin(frac{1}{x})}{x^2}dx
$$
I tried to use Dirichlet theorm but without any success. How can I show it without using taylor?

Sameer Baheti · Answer

HINT
Substitute $frac1xrightarrow t$ to get $int_1^{infty}sin(t)dt$

How to show that $ int_0^1frac{sin(frac{1}{x})}{x^2}dx$ diverges?

One Answer

Add your own answers!

Ask a Question