Integral dari $$$\sin{\left(6 c \right)}$$$

Temukan $$$\int \sin{\left(6 c \right)}\, dc$$$.

Misalkan $$$u=6 c$$$.

Kemudian $$$du=\left(6 c\right)^{\prime }dc = 6 dc$$$ (langkah-langkah dapat dilihat di »), dan kita memperoleh $$$dc = \frac{du}{6}$$$.

Dengan demikian,

$${\color{red}{\int{\sin{\left(6 c \right)} d c}}} = {\color{red}{\int{\frac{\sin{\left(u \right)}}{6} d u}}}$$

Terapkan aturan pengali konstanta $$$\int c f{\left(u \right)}\, du = c \int f{\left(u \right)}\, du$$$ dengan $$$c=\frac{1}{6}$$$ dan $$$f{\left(u \right)} = \sin{\left(u \right)}$$$:

$${\color{red}{\int{\frac{\sin{\left(u \right)}}{6} d u}}} = {\color{red}{\left(\frac{\int{\sin{\left(u \right)} d u}}{6}\right)}}$$

Integral dari sinus adalah $$$\int{\sin{\left(u \right)} d u} = - \cos{\left(u \right)}$$$:

$$\frac{{\color{red}{\int{\sin{\left(u \right)} d u}}}}{6} = \frac{{\color{red}{\left(- \cos{\left(u \right)}\right)}}}{6}$$

Ingat bahwa $$$u=6 c$$$:

$$- \frac{\cos{\left({\color{red}{u}} \right)}}{6} = - \frac{\cos{\left({\color{red}{\left(6 c\right)}} \right)}}{6}$$

Oleh karena itu,

$$\int{\sin{\left(6 c \right)} d c} = - \frac{\cos{\left(6 c \right)}}{6}$$

Tambahkan konstanta integrasi:

$$\int{\sin{\left(6 c \right)} d c} = - \frac{\cos{\left(6 c \right)}}{6}+C$$

$$$\int \sin{\left(6 c \right)}\, dc = - \frac{\cos{\left(6 c \right)}}{6} + C$$$A