求定积分∫(sinx-cosx)/3次根号下(sinx+cosx) [0,π/2]

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求定积分∫(sinx-cosx)/3次根号下(sinx+cosx)[0,π/2]求定积分∫(sinx-cosx)/3次根号下(sinx+cosx)[0,π/2]求定积分∫(sinx-cosx)/3次根

求定积分∫(sinx-cosx)/3次根号下(sinx+cosx) [0,π/2]
求定积分∫(sinx-cosx)/3次根号下(sinx+cosx) [0,π/2]

求定积分∫(sinx-cosx)/3次根号下(sinx+cosx) [0,π/2]
[0,π/2] ∫(sinx-cosx)/(sinx+cosx)^(1/3) dx
=[0,π/2] ∫-d(sinx+cosx)/(sinx+cosx)^(1/3)
=[0,π/2] ∫-d(sinx+cosx)/(sinx+cosx)^(1/3)
=-3/2 (sinx+cosx)^(2/3)|[0,π/2]
=0