integral from 0 to 2 of cos(t^2)

解

\int_{0}^{2} cos (t^{2}) d t

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

解答ステップ

\int_{0}^{2} cos (t^{2}) d t

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} t)]_{0}^{2}

限度を計算する:

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

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