Cho f'(x) = 2x - cos 2x . Tìm f(x) biết f(0) =0

12/22

Cho \[f'\left( x \right) = 2x - \cos 2x\]. Tìm \[f\left( x \right)\] biết \[f\left( 0 \right) = 0\].

\(f\left( x \right) = \frac{{{x^2}}}{2} - \frac{1}{2}\sin 2x\).

\(f\left( x \right) = {x^2} + \frac{1}{2}\sin 2x\).

\(f\left( x \right) = {x^2} - \frac{1}{2}\sin 2x\).

\(f\left( x \right) = {x^2} + \sin 2x\).

Giải thích

Ta có \[f\left( x \right) = \int {f'\left( x \right){\rm{dx}}} = \int {\left( {2x - \cos 2x} \right){\rm{d}}x} = {x^2} - \frac{1}{2}\sin 2x + C\].

Mà \[f\left( 0 \right) = 0 \Rightarrow C = 0\]. Vậy \(f\left( x \right) = {x^2} - \frac{1}{2}\sin 2x\).