移到一邊,積分限內(nèi)：
(x-π/2)f(sinx)
令x-π/2=p
pf(Cosp),P積分限為-π/2至π/2,p為奇函數(shù),f(Cosp)為偶函數(shù),pf(Cosp)為奇函數(shù),對(duì)稱區(qū)間中積分為0.你好，我有一個(gè)疑問(wèn)就是——p為奇函數(shù)？是怎么看出的？x-π/2=p，那么P不就是單調(diào)遞增的直線嗎？f(p)=pf(-p)=-p=-f(p),奇函數(shù)變量代換后，積分已經(jīng)由針對(duì)x變?yōu)獒槍?duì)p了，并針對(duì)[-π/2,π/2]區(qū)間進(jìn)行積分?？梢赃@樣理解嗎？針對(duì)積分區(qū)間p [-π/2,π/2]區(qū)間,f(p)=f(π/2)=π/2,f(-p)=f(-π/2)=-π/2=-f(π/2)=-f(p)f(-p)=-f(p),這是奇函數(shù)的特征，不針對(duì)某區(qū)間成立，對(duì)整個(gè)定義域都成立。奇函數(shù)沿Y軸反對(duì)稱，【積分區(qū)間沿Y軸對(duì)稱時(shí)】積分時(shí)兩側(cè)面積相同，符號(hào)相反，互相抵消。