integral from 2 to 5 of (1-x^2)-(11-7x)

解答

\int_{2}^{5} (1 - x^{2}) - (11 - 7 x) d x

\frac{9}{2}

十进制

4.5

求解步骤

\int_{2}^{5} 1 - x^{2} - (11 - 7 x) d x

化简

= \int_{2}^{5} - x^{2} + 7 x - 10 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_{2}^{5} x^{2} d x + \int_{2}^{5} 7 x d x - \int_{2}^{5} 10 d x

\int_{2}^{5} x^{2} d x = 39

\int_{2}^{5} 7 x d x = \frac{147}{2}

\int_{2}^{5} 10 d x = 30

= - 39 + \frac{147}{2} - 30

化简

- 39 + \frac{147}{2} - 30 : \frac{9}{2}

= \frac{9}{2}

\int \frac{1}{x ^{\frac{3}{4}}} d x

x \to 0 lim (2^{\frac{1}{2}})

\int_{5}^{\infty} e^{- \frac{x}{4}} d x

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\int 1 + x^{3} d x