x∈[0,π/4],sinx∈[0,√2/2]
0 < ∫[0,π/4] (sinx)^n dx < (π/4) * (√2/2)^n
lim(n->∞) (√2/2)^n = 0
由迫敛准则(夹逼准则),
原式 = 0