integral from pi/5 to pi of |cos(x)|

解

\int_{\frac{π}{5}}^{π} ∣ cos (x) ∣ d x

- \frac{5 - 5}{2 2} + 2

十進法表記

1.41221 \dots

解答ステップ

\int_{\frac{π}{5}}^{π} ∣ cos (x) ∣ d x

絶対数を排除する

= \int_{\frac{π}{5}}^{\frac{π}{2}} cos (x) d x + \int_{\frac{π}{2}}^{π} - cos (x) d x

\int_{\frac{π}{5}}^{\frac{π}{2}} cos (x) d x = 1 - \frac{5 - 5}{2 2}

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

= 1 - \frac{5 - 5}{2 2} + 1

簡素化

= - \frac{5 - 5}{2 2} + 2