求极限lim(x→∞)定积分sin^nxdx x∈[0,π/4]

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求极限lim(x→∞)定积分sin^nxdxx∈[0,π/4]求极限lim(x→∞)定积分sin^nxdxx∈[0,π/4]求极限lim(x→∞)定积分sin^nxdxx∈[0,π/4]x∈[0,π/

求极限lim(x→∞)定积分sin^nxdx x∈[0,π/4]
求极限lim(x→∞)定积分sin^nxdx x∈[0,π/4]

求极限lim(x→∞)定积分sin^nxdx x∈[0,π/4]
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