Need a bit of help.
Show that ∫1 to ∞ (|sin x|/x^2) dx is convergent.

Question

Need a bit of help.
Show that ∫1 to ∞  (|sin x|/x^2) dx is convergent.

sirm3d · Answer

compare the integrand with a series that is known to be convergent.

anonymous · Answer

I guess that's not really what I need help with, and I should have done better to write my true question better. I do know that I need to find one that converges. How would I compare it with a convergent integral and show it on paper?

sirm3d · Answer

sin x is bounded above by 1, so $$\large \frac{ \left| \sin x \right| }{ x^2 } \le \frac{ 1 }{ x^2 }$$ if the improper integral of the RHS is a value (hence convergent), your integrand problem is also convergent.
a trick with sine and consine functions is to replace them by a number, usually 1 as an upper bound

anonymous · Answer

still any doubts........?

anonymous · Answer

u can ask