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

解答

\int_{0}^{π} cos (x^{2}) d x

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

求解步骤

\int_{0}^{π} cos (x^{2}) d x

这是非初等函数积分:

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

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

带入上下限计算后得:

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

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

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