数学定积分

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xjskakjs

2025-12-30 16:10

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另X=sint,则-π/2≤t≤π/2,dx=costdt

原式=∫cost*costdt(下限-π/2,上限π/2)=∫(cos2t+1)/2dt(下限-π/2,上限π/2)=

[1/4*sin2t+t/2](下限-π/2,上限π/2)=(1/4sinπ+π/4)-(1/4sin-π+(/π/4))=π/2

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