Wednesday, June 8, 2016

calculus - Convergence of the integral inti0nftyfracsin2xx2 mathrmdx.




Determine whether the integral 0sin2xx2 dx

converges.





I know it converges, since in general we can use complex analysis, but I'd like to know if there is a simpler method that doesn't involve complex numbers. But I cannot come up with a function that I could compare the integral with.


Answer



Hint:$$x>1\implies0\le\frac{\sin^2(x)}{x^2}\le\frac1{x^2}\\0

No comments:

Post a Comment

analysis - Injection, making bijection

I have injection f:AB and I want to get bijection. Can I just resting codomain to f(A)? I know that every function i...