$$$\epsilon$$$에 대한 $$$\frac{2 \epsilon r^{2}}{5}$$$의 적분

$$$\int \frac{2 \epsilon r^{2}}{5}\, d\epsilon$$$을(를) 구하시오.

상수배 법칙 $$$\int c f{\left(\epsilon \right)}\, d\epsilon = c \int f{\left(\epsilon \right)}\, d\epsilon$$$을 $$$c=\frac{2 r^{2}}{5}$$$와 $$$f{\left(\epsilon \right)} = \epsilon$$$에 적용하세요:

$${\color{red}{\int{\frac{2 \epsilon r^{2}}{5} d \epsilon}}} = {\color{red}{\left(\frac{2 r^{2} \int{\epsilon d \epsilon}}{5}\right)}}$$

멱법칙($$$\int \epsilon^{n}\, d\epsilon = \frac{\epsilon^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$)을 $$$n=1$$$에 적용합니다:

$$\frac{2 r^{2} {\color{red}{\int{\epsilon d \epsilon}}}}{5}=\frac{2 r^{2} {\color{red}{\frac{\epsilon^{1 + 1}}{1 + 1}}}}{5}=\frac{2 r^{2} {\color{red}{\left(\frac{\epsilon^{2}}{2}\right)}}}{5}$$

따라서,

$$\int{\frac{2 \epsilon r^{2}}{5} d \epsilon} = \frac{\epsilon^{2} r^{2}}{5}$$

적분 상수를 추가하세요:

$$\int{\frac{2 \epsilon r^{2}}{5} d \epsilon} = \frac{\epsilon^{2} r^{2}}{5}+C$$

$$$\int \frac{2 \epsilon r^{2}}{5}\, d\epsilon = \frac{\epsilon^{2} r^{2}}{5} + C$$$A