integral from 0 to pi/4 of cos(x^2)

解

\int_{0}^{\frac{π}{4}} cos (x^{2}) d x

\frac{π}{2} C (\frac{2}{π} \frac{π}{4}) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

解答ステップ

\int_{0}^{\frac{π}{4}} cos (x^{2}) d x

非初等積分を使用する:

\int cos (x^{2}) d x = \frac{π}{2} C (\frac{2}{π} x)

= [\frac{π}{2} C (\frac{2}{π} x)]_{0}^{\frac{π}{4}}

限度を計算する:

\frac{π}{2} C (\frac{2}{π} \frac{π}{4}) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

= \frac{π}{2} C (\frac{2}{π} \frac{π}{4}) - \frac{π}{2} C (\frac{2}{π} \cdot 0)