Giải thích các bước giải:
1.Ta có:
$\dfrac14=\displaystyle\int^m_0\sin x\cos xdx$
$\to \dfrac14=\displaystyle\int^m_0\sin xd(\sin x)$
$\to \dfrac14=\dfrac12\sin^2x\Bigg|^m_0$
$\to \dfrac14=\dfrac12\sin^2m-\dfrac12\sin^20$
$\to \dfrac14=\dfrac12\sin^2m-0$
$\to \dfrac14=\dfrac12\sin^2m$
$\to \sin^2m=\dfrac12$
$\to \sin m=\pm\sqrt{\dfrac12}$
$\to m=\dfrac{\pi}{4}+\dfrac{k\pi}{2}$
2.Ta có:
$0=\displaystyle\int^m_0 \cos2xdx$
$\to 0=\dfrac12\displaystyle\int^m_0 \cos2xd(2x)$
$\to 0=\displaystyle\int^m_0 \cos2xd(2x)$
$\to 0=\sin2x\Bigg|^m_0$
$\to 0=\sin(2m)-\sin 0$
$\to \sin2m=0$
$\to 2m=k\pi$
$\to m=\dfrac{k\pi}{2}$
