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

解答

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

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

求解步骤

\int_{0}^{x} 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}^{x}

带入上下限计算后得:

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

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

\int_{0}^{2} x^{2} (x^{3} + 1) d x

\int_{\frac{π}{2}}^{0} cos (x) d x

\int_{1}^{2} \frac{1}{x ( 1 + x ^{4} )} d x

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\int_{0}^{\frac{π}{3}} sec (θ) tan (θ) d θ