- #1
Tricore
- 21
- 0
I am trying to prove that [tex]\int_0^{\pi/4} (\tan x)^{-\alpha} dx[/tex] is finite for [tex]0 < \alpha < 1[/tex], where the integral denotes the Lebesgue integral with the Lebesgue measure. I've decided wether it converges for all other values of [tex]\alpha\in\mathbb{R}[/tex], but am simply stuck with this one.
I've tried using monotone convergence to integrate over the closed interval from 1/n to pi/4, where I can use the Riemann integral, but I can't figure out how to find an anti-derivative for the function. I've also tried finding a larger, integrable function but without luck.
Any hints would be much appreciated.
I've tried using monotone convergence to integrate over the closed interval from 1/n to pi/4, where I can use the Riemann integral, but I can't figure out how to find an anti-derivative for the function. I've also tried finding a larger, integrable function but without luck.
Any hints would be much appreciated.