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

Mathematics Asked by abuka123 on November 26, 2021

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?

One Answer

HINT

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

Answered by Sameer Baheti on November 26, 2021

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