证明：∫(sinx/x)dx=∫dx/arccosx.左边上限派/2,下限派/3；右边上限1/2,下限0.没分了，请见谅！

Question

证明：∫ (sinx / x )dx=∫ dx/arccosx.左边上限派/2,下限派/3；右边上限1/2,下限0.
没分了，请见谅！

Answer 1

右边作变换t＝arccosx,则x＝cost,dx＝－sintdt.
x＝0时,t＝π/2,x＝1/2时,t＝π/3
所以,
∫(0→1/2) dx/arccosx
＝∫(π/2→π/3) (-sint)dt/t
＝∫(π/3→π/2) (sint/t) dt
证毕!