用分部积分法求定积分？
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(4)
∫(0->1) te^(-2t) dt
=-(1/2)∫(0->1) t de^(-2t)
=-(1/2)[ t.e^(-2t)]|(0->1)+(1/2)∫(0->1) e^(-2t) dt
=-(1/2)e^(-2) -(1/4)[ e^(-2t)]|(0->1)
=-(1/2)e^(-2) -(1/4)[ e^(-2) -1 ]
=1/4 - (3/4)e^(-2)
(2)
∫(0->π/2) xcos(x/2) dx
=2∫(0->π/2) x dsin(x/2)
=2[x.sin(x/2)]|(0->π/2) -2 ∫(0->π/2) sin(x/2) dx
=2(π/2)(√2/2) +4[cos(x/2)]|(0->π/2)
=(√2/2)π +4 ( √2/2 -1 )
=(√2/2)π +2√2 -4
∫(0->1) te^(-2t) dt
=-(1/2)∫(0->1) t de^(-2t)
=-(1/2)[ t.e^(-2t)]|(0->1)+(1/2)∫(0->1) e^(-2t) dt
=-(1/2)e^(-2) -(1/4)[ e^(-2t)]|(0->1)
=-(1/2)e^(-2) -(1/4)[ e^(-2) -1 ]
=1/4 - (3/4)e^(-2)
(2)
∫(0->π/2) xcos(x/2) dx
=2∫(0->π/2) x dsin(x/2)
=2[x.sin(x/2)]|(0->π/2) -2 ∫(0->π/2) sin(x/2) dx
=2(π/2)(√2/2) +4[cos(x/2)]|(0->π/2)
=(√2/2)π +4 ( √2/2 -1 )
=(√2/2)π +2√2 -4
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