integral from 10 to 13 of xsqrt(x-9)

解答

\int_{10}^{13} x x - 9 d x

\frac{272}{5}

十进制

54.4

求解步骤

\int_{10}^{13} x x - 9 d x

使用换元积分法

= \int_{1}^{4} (u + 9) u d u

乘开

(u + 9) u : u^{\frac{3}{2}} + 9 u

= \int_{1}^{4} u^{\frac{3}{2}} + 9 u d u

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}^{4} u^{\frac{3}{2}} d u + \int_{1}^{4} 9 u d u

\int_{1}^{4} u^{\frac{3}{2}} d u = \frac{62}{5}

\int_{1}^{4} 9 u d u = 42

= \frac{62}{5} + 42

化简

\frac{62}{5} + 42 : \frac{272}{5}

= \frac{272}{5}

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