integral from 0 to 0.5 of 7arccos(x)

解

\int_{0}^{0.5} 7 arccos (x) d x

4.60301 \dots

解答ステップ

\int_{0}^{0.5} 7 arccos (x) d x

定数を除く:

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

= 7 \cdot \int_{0}^{0.5} arccos (x) d x

部分積分を適用する

= 7 [x arccos (x) - \int - \frac{x}{1 - x ^{2}} d x]_{0}^{0.5}

\int - \frac{x}{1 - x ^{2}} d x = 1 - x^{2}

= 7 [x arccos (x) - 1 - x^{2}]_{0}^{0.5}

限度を計算する:

0.65757 \dots

= 7 \cdot 0.65757 \dots

簡素化

= 4.60301 \dots