integral from 0 to 1.1 of sin(x^2)

解答

\int_{0}^{1.1} sin (x^{2}) d x

1.25331 \dots § (\frac{2}{π} \cdot 1.1) - 1.25331 \dots § (\frac{2}{π} \cdot 0)

求解步骤

\int_{0}^{1.1} sin (x^{2}) d x

这是非初等函数积分:

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

= [\frac{π}{2} § (\frac{2}{π} x)]_{0}^{1.1}

化简

= [1.25331 \dots § (\frac{2}{π} x)]_{0}^{1.1}

带入上下限计算后得:

1.25331 \dots § (\frac{2}{π} \cdot 1.1) - 1.25331 \dots § (\frac{2}{π} \cdot 0)

= 1.25331 \dots § (\frac{2}{π} \cdot 1.1) - 1.25331 \dots § (\frac{2}{π} \cdot 0)

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