Hi, Sorry but I have more questions...
1. If Im, n=∫sinmx cosnx dx, prove that
Im, n=∫sinm-1x (d/dx)[(-cosn+1x)/(n+1)] dx = [-sinm-1x cosn+1x]/(n+1) + (m-1)/(n+1)[Im-2,n - Im,n]
Hence show that Im, n = [-sinm-1x cosn+1x]/(n+1) + (m-1)/(n+1)*Im-2,n
2. If Un=∫0pi/2 θsinnθdθ, n>1 prove that...