大师作文网高数定积分计算一道,证明不用证了,我会,
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高数定积分计算一道,
证明不用证了,我会,
证明不用证了,我会,
把π当成2a、xsinx/(1+cos^2(x))当成f(x)就行了
原式=∫(0→π/2)[xsinx/(1+cos^2(x))+(π-x)sin(π-x)/(1+cos^2(π-x))]dx
=∫(0→π/2)[xsinx/(1+cos^2(x))+(π-x)sinx/(1+cos^2(x))]dx
=π∫(0→π/2)sinx/(1+cos^2(x))dx
=-π∫(0→π/2)d(cosx)/(1+cos^2(x))
=-πarctan(cosx)|(0→π/2)
=π^2/4
原式=∫(0→π/2)[xsinx/(1+cos^2(x))+(π-x)sin(π-x)/(1+cos^2(π-x))]dx
=∫(0→π/2)[xsinx/(1+cos^2(x))+(π-x)sinx/(1+cos^2(x))]dx
=π∫(0→π/2)sinx/(1+cos^2(x))dx
=-π∫(0→π/2)d(cosx)/(1+cos^2(x))
=-πarctan(cosx)|(0→π/2)
=π^2/4