integral from 0 to 5 of (25-x^2)

解答

\int_{0}^{5} (25 - x^{2}) d x

\frac{250}{3}

十进制

83.33333 \dots

求解步骤

\int_{0}^{5} 25 - x^{2} d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{5} 25 d x - \int_{0}^{5} x^{2} d x

\int_{0}^{5} 25 d x = 125

\int_{0}^{5} x^{2} d x = \frac{125}{3}

= 125 - \frac{125}{3}

化简

125 - \frac{125}{3} : \frac{250}{3}

= \frac{250}{3}

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