Question

F(x)=∫0到x cos(x^2-t)dt 求F(x)的导数

Answer 1

令u=x²-t
则dt=-du
原式可变为
F(x)=-∫(x²到x²-x)cosudu
所以
F'(x)=-(2x-1)cos(x²-x)+2xcos(x²)

Answer 2

cos(x^2-t)=cos(x^2)cost+sin(x^2)sint
F(x)=cos(x^2)sin(x)+sin(x^2)[1-cos(x)]=sin(x^2)-sin(x^2-x)
F'(X)=2xcos(x^2)-(2x-1)cos(x^2-x)