求,不定积分.∫上限兀/2 下限0(cosx/2-sinx/2)dx+∫上限 兀下限 兀/2(sinx/2-cosx/2
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求,不定积分.∫上限兀/2 下限0(cosx/2-sinx/2)dx+∫上限 兀下限 兀/2(sinx/2-cosx/2)dx
![求,不定积分.∫上限兀/2 下限0(cosx/2-sinx/2)dx+∫上限 兀下限 兀/2(sinx/2-cosx/2](/uploads/image/z/5120596-28-6.jpg?t=%E6%B1%82%2C%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86.%E2%88%AB%E4%B8%8A%E9%99%90%E5%85%80%2F2+%E4%B8%8B%E9%99%900%EF%BC%88cosx%2F2-sinx%2F2%EF%BC%89dx%2B%E2%88%AB%E4%B8%8A%E9%99%90+%E5%85%80%E4%B8%8B%E9%99%90+%E5%85%80%2F2%EF%BC%88sinx%2F2-cosx%2F2)
∫(0,兀/2)(cosx/2-sinx/2)dx+∫(兀/2.兀)(sinx/2-cosx/2)dx
=2[∫(0,兀/2)(cosx/2-sinx/2)dx/2+∫(兀/2.兀)(sinx/2-cosx/2)dx/2 ]
=2(sinx/2+cosx/2)|(0,兀/2)-2(sinx/2+cosx/2)|(兀/2.兀)
=2(√2-1)-2(1-√2)
=4(√2-1)
=2[∫(0,兀/2)(cosx/2-sinx/2)dx/2+∫(兀/2.兀)(sinx/2-cosx/2)dx/2 ]
=2(sinx/2+cosx/2)|(0,兀/2)-2(sinx/2+cosx/2)|(兀/2.兀)
=2(√2-1)-2(1-√2)
=4(√2-1)
求,不定积分.∫上限兀/2 下限0(cosx/2-sinx/2)dx+∫上限 兀下限 兀/2(sinx/2-cosx/2
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