判断定积分的正负,如图…

【0,π】∫(1+sin²t)d(sin2t)=【0,π】[sin2t+∫sin²td(sin2t)]=【0,π】∫sin²td(sin2t)
=【0,π】(1/2)∫(1+cos2t)d(sin2t)=【0,π】[(1/2)sin2t+(1/2)∫(cos2td(sin2t)]
=【0,π】(1/2)∫(cos2td(sin2t)=【0,π】(1/2)[cos2tsin2t+2∫sin²2tdt]
=【0,π】∫sin²2tdt=【0,π】(1/2)∫(1+cos4t)dt=【0,π】(1/2)[t+(1/4)∫cos4td(4t)]
=(1/2)[t+(1/4)sin4t]【0,π】=(1/2)π
是正值.

先用倍角公式化简括号里的东西。然后再判断

嘛意思，没懂