sinsinx函数积分求导|(PI/2,-PI/2)-sinsinxdx=0看过|(PI/2,-PI/2)-sinsinxdx=0,"|"代替那个积分符号.sinsinx的原函数是什么?哪位详说下,感激不尽.我自己求是对方程两边求导,则左边是sinsinx|(PI/2,-PI/2)=2

Question

sinsinx 函数积分求导|(PI/2,-PI/2) -sinsinx dx = 0
看过|(PI/2,-PI/2) -sinsinx dx = 0 ,"|"代替那个积分符号.sinsinx的原函数是什么?哪位详说下,感激不尽.我自己求是对方程两边求导,则左边是 sinsinx|(PI/2,-PI/2)=2sin1,难道我算错了?还是左边=cosxsinsinx,记得|f(x)dx对它进行求导=f(x)的呀.x|f(x)dx对它进行求导=xf(x)+|f(x)dx

Answer 1

F(x)=sin(sinx) F(x)=-F(-x) ∫[-π/2,π/2]F(x)dx=∫[-π/2,0]F(x)dx+∫[0,π/2]F(x)dx =-∫[0,π/2]F(x)dx+∫[0,π/2]F(x)dx =0