Recent content by k1902

Apologies for that, here's the cleaned up, comprehensible version of the question (thanks to Mark44): Let ##I_n = \int_0^{\pi/2} x \cos^n(x) dx##, with ##n \ge 0## i) Show that ##n I_n = (n - 1)I_{n-2} - n^{- 1}##, for ##n \ge 2##. ii) Find the exact value of ##I_3##.

Sorry, I'm new here and have no idea how to format the text. But yes that's what I was trying to write , except part i) is i) Show that ##n I_n = (n - 1)I_{n-2} - n^{- 1}##, for ##n \ge 2##. Thanks for the help with formatting :)

Homework Statement Let In = ∫x(cos^n(x)) with limits between x=π/2, x=0 for n≥0 i) Show that nIn=(n-1)In-2 -n^-1 for n≥2 ii) Find the exact value of I3 Homework Equations ∫u'v = uv-∫uv' is what I use for these questions The Attempt at a Solution Rewritten as ∫ xcos^n-1(x) cosx u'=cosx...