integral from 0 to 1 of cos(x^4)

解

\int_{0}^{1} cos (x^{4}) d x

- \frac{1}{8} (E_{\frac{3}{4}} (1 i) + E_{\frac{3}{4}} (- 1 i))

解答ステップ

\int_{0}^{1} cos (x^{4}) d x

非初等積分を使用する:

\int cos (x^{4}) d x = - \frac{1}{8} x (E_{\frac{3}{4}} (- i x^{4}) + E_{\frac{3}{4}} (i x^{4}))

= [- \frac{1}{8} x (E_{\frac{3}{4}} (- i x^{4}) + E_{\frac{3}{4}} (i x^{4}))]_{0}^{1}

限度を計算する:

- \frac{1}{8} (E_{\frac{3}{4}} (1 i) + E_{\frac{3}{4}} (- 1 i))

= - \frac{1}{8} (E_{\frac{3}{4}} (1 i) + E_{\frac{3}{4}} (- 1 i))