Question

计算分段函数定积分

上（100/X平方，X>100）下（0，X<=100）麻烦详细点

Answer 1

原式=∫(0,√3) t/(1+t^2)dt
=(1/2)*∫(0,√3) d(1+t^2)/(1+t^2)
=(1/2)*ln|1+t^2||(0,√3)
=ln2
（3）令t=x-π/2，x=t+π/2，dx=dt
原式=∫(-π/2,π/2) √[1+cos(2t+π)]dt
=∫(-π/2,π/2) √(1-cos2t)dt
=2*∫(0,π/2) √(1-cos2t)dt
=2√2*∫(0,π/2) costdt
=2√2*sint|(0,π/2)
=2√2

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