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高等数学求积分,我的做法错在哪里了?
3个回答
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I=2∫(0,π/4) (2cos²t–1)dt+2∫(π/4,3π/4) (1–2cos²t)dt+2∫(3π/4,π) (2cos²t–1)dt
=2∫(0,π/4) cos2tdt+2∫(π/4,3π/4) (–cos2t)dt+2∫(3π/4,π) cos2tdt
=sin2t|(0,π/4) –sin2t|(π/4,3π/4)+sin2t|(3π/4,π)
=(1–0)–(–1–1)+(0+1)
=4
=2∫(0,π/4) cos2tdt+2∫(π/4,3π/4) (–cos2t)dt+2∫(3π/4,π) cos2tdt
=sin2t|(0,π/4) –sin2t|(π/4,3π/4)+sin2t|(3π/4,π)
=(1–0)–(–1–1)+(0+1)
=4
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