多选若果∫df(x)=∫dg(x),则必有A.f'(x)=g'(x)B.df(x)=dg(x)C.f(x)=g(x)D.d[∫f'(x)dx]=[∫g'(x)dx]

Question

多选 若果∫df(x)=∫dg(x),则必有
A.f'(x)=g'(x)
B.df(x)=dg(x)
C.f(x)=g(x)
D.d[∫f'(x)dx]=[∫g'(x)dx]

Answer 1

∫ d[f(x)] = f(x) + C
∫ d[g(x)] = g(x) + D
∫ d[f(x)] = ∫ d[g(x)]
==> f(x) = g(x) + D - C,∴f(x) ≠ g(x),C错误
f'(x) = g'(x),∴A正确,B正确
d[∫ f'(x) dx] = d[ f(x) + C ] = f'(x) dx
而∫ g'(x) dx = g(x) + D,∴D错误
若是d[ ∫g'(x) dx] = d[ g(x) + D] = g'(x) dx,则D正确