作业帮定积分.
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定积分.
定积分.
定积分.
所以f(π/2)=arctan[sin(π/2)]=π/4
后边的x变成t吧
f(x)=ʃ(0-->x)cost/(1+sin²t)dt
=ʃ(0-->x)dsint/(1+sin²t)
=arctan(sint)|(0-->x)
=arctan(sinx)
f(π/2)=arctan(sinπ/2)=arctan1=π/4
∫<0.π/2>1/1+sinx^2dsinx=arctansinx=π/4
原式f(x)=∫dsinx/(1+sin²x),(0-->x)
=arctan(sinx),(0-->x)
f(Pai/2)=arctansinPai/2-arctansin0=Pai/4.