Question

一道定积分的问题

sinx+cosx分之sinx的定积分

若以下回答无法解决问题，邀请你更新回答

Answer 1

原式=½∫[0，π/2](sinx+cosx+sinx-cosx)/(sinx+cosx)  dx

=½∫[0，π/2] [1+(sinx-cosx)/(sinx+cosx)]dx

=½∫[0，π/2]dx+½∫[0，π/2](sinx-cosx)/(sinx+cosx)dx

=π/4 - ½∫[0，π/2]d(sinx+cosx)/(sinx+cosx)

=π/4 - ½ln(sinx+cosx)|[0,π/2]

=π/4 - ½(ln1 - ln1)

=π/4

Answer 2

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