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高数题,设f(x)在[0,1]上连续,且f(x)>0
记I1=∫(0,1)f(x)dx,I2=∫(0,π/2)f(sinx)dx,I3=∫(0,π/4)f(tanx)dx,则有AI1<I2<I3BI3<I1<I2CI2<I3...
记I1=∫(0,1)f(x)dx,I2=∫(0,π/2)f(sinx)dx,I3=∫(0,π/4)f(tanx)dx,则有
AI1<I2<I3 BI3<I1<I2 CI2<I3<I1 DI1<I3<I2 展开
AI1<I2<I3 BI3<I1<I2 CI2<I3<I1 DI1<I3<I2 展开
1个回答
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l2:作换元sinx=t l2=∫(0,1)f(t)darcsint=∫(0,1)f(t)dt/√(1-t^2) >∫(0,1)f(t)dt=l1 (因f(t)/√(1-t^2) > f(t)
l3:同理做换元tanx=t l3=∫(0,1)f(t)dt/(1+t^2) <∫(0,1)f(t)dt=l1 (同理)
故l3<l1<l2.选B
l3:同理做换元tanx=t l3=∫(0,1)f(t)dt/(1+t^2) <∫(0,1)f(t)dt=l1 (同理)
故l3<l1<l2.选B
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