引用:
原帖由 MAJIADI 於 2025-4-28 11:55 發表 
114鳳新高中
7474
第 9 題 (3) 也才一分，太難賺了
I_n + I_(n+2)
=∫ {0 to π/4} [ (tanx)^n + (tanx)^(n+2) ] dx
=∫ {0 to π/4} [(tanx)^n*(1+(tanx)^2)]dx
=∫ {0 to π/4} (tanx)^n*(secx)^2 dx
=∫ {0 to π/4} (tanx)^n*d(tanx)
=[1/(n+1)]*(tanx)^(n+1) | {0 to π/4}
=1/(n+1)
