integral from 1 to 2 of (1-x^2)-(3-3x)

解答

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

\frac{1}{6}

十进制

0.16666 \dots

求解步骤

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

化简

= \int_{1}^{2} - x^{2} + 3 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_{1}^{2} x^{2} d x + \int_{1}^{2} 3 x d x - \int_{1}^{2} 2 d x

\int_{1}^{2} x^{2} d x = \frac{7}{3}

\int_{1}^{2} 3 x d x = \frac{9}{2}

\int_{1}^{2} 2 d x = 2

= - \frac{7}{3} + \frac{9}{2} - 2

化简

- \frac{7}{3} + \frac{9}{2} - 2 : \frac{1}{6}

= \frac{1}{6}

\frac{d x}{d t} = x^{2} - 6 x + 14

d er i v a t i v e f (x) = 2 x^{4} + x^{3} - x^{2} + 4

\int_{0}^{x} 1 + 9 t d t

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