定积分 cosx-sinx|60` 30`=0
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[π/6..π/3]∫(cosx-sinx)dx
=[π/6..π/3]∫√2 sin(x+3π/4)dx
=-√2 cos(x+3π/4)|[π/6..π/3]
=-√2 cos(13π/12)+√2 cos(11π/12)
=0
√2 sin(x-π/4)=√2 (sinxcosπ/4-cosxsinπ/4)=sinx-cosx
=[π/6..π/3]∫√2 sin(x+3π/4)dx
=-√2 cos(x+3π/4)|[π/6..π/3]
=-√2 cos(13π/12)+√2 cos(11π/12)
=0
√2 sin(x-π/4)=√2 (sinxcosπ/4-cosxsinπ/4)=sinx-cosx
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