integral from 0 to 1 of (x^4-3x^3+1)

解答

\int_{0}^{1} (x^{4} - 3 x^{3} + 1) d x

\frac{9}{20}

十进制

0.45

求解步骤

\int_{0}^{1} x^{4} - 3 x^{3} + 1 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}^{1} x^{4} d x - \int_{0}^{1} 3 x^{3} d x + \int_{0}^{1} 1 d x

\int_{0}^{1} x^{4} d x = \frac{1}{5}

\int_{0}^{1} 3 x^{3} d x = \frac{3}{4}

\int_{0}^{1} 1 d x = 1

= \frac{1}{5} - \frac{3}{4} + 1

化简

\frac{1}{5} - \frac{3}{4} + 1 : \frac{9}{20}

= \frac{9}{20}

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