Đáp án: $C$
Giải thích các bước giải:
Ta có:
$f'(x)=\cos x\cos^22x$
$\to f(x)=\displaystyle\int f'(x)dx=\displaystyle\int \cos x\cos^22xdx$
$\to f(x)=\displaystyle\int(1-2sin^2x)^2d(\sin x)$
$\to f(x)=\displaystyle\int1-4sin^2x+4\sin^4xd(\sin x)$
$\to f(x)=\sin x-\dfrac43\sin^3x+\dfrac45\sin^5x+C$
Mà $f(0)=0\to C=0$
$\to f(x)=\sin x-\dfrac43\sin^3x+\dfrac45\sin^5x$
$\to \displaystyle\int^{\pi}_0f(x)dx=\displaystyle\int^{\pi}_0\sin x-\dfrac43\sin^3x+\dfrac45\sin^5xdx$
Bấm máy
$\to \displaystyle\int^{\pi}_0f(x)dx=\dfrac{242}{225}$
