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24求微积分计算题计算过程和答案.谢谢
2个回答
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∫(0,π/2)xsinx dx+∫(0,π/2)xcosx dx
=-∫(0,π/2)xd cosx +∫(0,π/2)xdsinx
=-xcosx I(0,π/2)+sinx I(0,π/2)+xsinx I(0,π/2)-cosx I(0,π/2)
=0+1+π/2+1
=2+π/2
∫(1,e)lnx dinx=(1/2)(lnx)^2 I(1,e)=1/2
=-∫(0,π/2)xd cosx +∫(0,π/2)xdsinx
=-xcosx I(0,π/2)+sinx I(0,π/2)+xsinx I(0,π/2)-cosx I(0,π/2)
=0+1+π/2+1
=2+π/2
∫(1,e)lnx dinx=(1/2)(lnx)^2 I(1,e)=1/2
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