I-0-pi-4-xtg-x-dx-

Question Number 162604 by amin96 last updated on 30/Dec/21

I = \int_{0}^{\frac{π}{4}} x t g (x) d x = ?

Answered by Ar Brandon last updated on 30/Dec/21

I = \int_{0}^{\frac{π}{4}} x \tan x d x

= - {[x \ln (\cos x)]}_{0}^{\frac{π}{4}} + \int_{0}^{\frac{π}{4}} \ln (\cos x) d x

= - \frac{π}{4} \ln (\frac{1}{\sqrt{2}}) + \frac{G}{2} - \frac{π \ln 2}{4} = \frac{G}{2} - \frac{π \ln 2}{8}