∫(0,π)(e^cosx-e^(-cosx))dx

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∫(0,π)(e^cosx-e^(-cosx))dx∫(0,π)(e^cosx-e^(-cosx))dx∫(0,π)(e^cosx-e^(-cosx))dx代换t=x-π/2,代入得:∫(0,π)(e

∫(0,π)(e^cosx-e^(-cosx))dx
∫(0,π)(e^cosx-e^(-cosx))dx

∫(0,π)(e^cosx-e^(-cosx))dx
代换t=x-π/2,代入得:∫(0,π)(e^cosx-e^(-cosx))dx =∫(-π/2,π/2)(e^cos(π/2+t)-e^(-cos(π/2+t))dt =∫(-π/2,π/2)(e^(-sint)-e^(sint))dt 由于被积函数是奇函数,区间对称,故积分为0