integral from 0 to 0.2 of sin^2(x)

解

\int_{0}^{0.2} sin^{2} (x) d x

0.00264 \dots

解答ステップ

\int_{0}^{0.2} sin^{2} (x) d x

三角関数の公式を使用して書き換える

= \int_{0}^{0.2} \frac{1 - cos ( 2 x )}{2} d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{0}^{0.2} 1 - cos (2 x) d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int_{0}^{0.2} 1 d x - \int_{0}^{0.2} cos (2 x) d x)

\int_{0}^{0.2} 1 d x = 0.2

\int_{0}^{0.2} cos (2 x) d x = 0.19470 \dots

= \frac{1}{2} (0.2 - 0.19470 \dots)

簡素化

\frac{1}{2} (0.2 - 0.19470 \dots) : 0.00264 \dots

= 0.00264 \dots