integral from 0 to sqrt(pi of)sin(x^2)

解

\int_{0}^{π} sin (x^{2}) d x

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

解答ステップ

\int_{0}^{π} sin (x^{2}) d x

非初等積分を使用する:

\int sin (x^{2}) d x = \frac{π}{2} § (\frac{2}{π} x)

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

限度を計算する:

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

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