对 $\int$ $f(\cos x) \sin x$ $\mathrm{d} x$ 凑微分的计算方法(B006)

问题

通过凑微分,如何计算 [$\textcolor{Orange}{\int f(\cos x) \sin x \mathrm{d} x}$] ?

选项

[A].   $\int$ $f(\cos x) \sin x$ $\mathrm{d} x$ $=$ $- \int$ $f(\cos x)$ $\mathrm{d} (\sin x)$

[B].   $\int$ $f(\cos x) \sin x$ $\mathrm{d} x$ $=$ $\int$ $f(\cos x)$ $\mathrm{d} (\cos x)$

[C].   $\int$ $f(\cos x) \sin x$ $\mathrm{d} x$ $=$ $- \int$ $f(\cos x)$ $\mathrm{d} (\cos x)$

[D].   $\int$ $f(\cos x) \sin x$ $\mathrm{d} x$ $=$ $\int$ $f(\cos x)$ $\mathrm{d} (\sin x)$



显示答案

$$\int \textcolor{Red}{f(\cos x)} \textcolor{Green}{\times} \textcolor{Red}{\sin x} \mathrm{d} \textcolor{Yellow}{x} =$$ $$\textcolor{Orange}{-} \int \textcolor{Red}{f(\cos x)} \mathrm{d} (\textcolor{Yellow}{\cos x}).$$

常用的几种凑微分形式: