integral from 0 to 1 of 4cos(x^2)

解

\int_{0}^{1} 4 cos (x^{2}) d x

4 (\frac{π}{2} C (\frac{2}{π} \cdot 1) - \frac{π}{2} C (\frac{2}{π} \cdot 0))

解答ステップ

\int_{0}^{1} 4 cos (x^{2}) d x

定数を除く:

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

= 4 \cdot \int_{0}^{1} 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)

= 4 [\frac{π}{2} C (\frac{2}{π} x)]_{0}^{1}

限度を計算する:

\frac{π}{2} C (\frac{2}{π} \cdot 1) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

= 4 (\frac{π}{2} C (\frac{2}{π} \cdot 1) - \frac{π}{2} C (\frac{2}{π} \cdot 0))