integral from 5 to 0 of |2x-5|

解答

\int_{5}^{0} ∣ 2 x - 5 ∣ d x

- \frac{25}{2}

十进制

- 12.5

求解步骤

\int_{5}^{0} ∣ 2 x - 5 ∣ d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{5} ∣ 2 x - 5 ∣ d x

拿掉绝对值

= - (\int_{0}^{\frac{5}{2}} - 2 x + 5 d x + \int_{\frac{5}{2}}^{5} 2 x - 5 d x)

\int_{0}^{\frac{5}{2}} - 2 x + 5 d x = \frac{25}{4}

\int_{\frac{5}{2}}^{5} 2 x - 5 d x = \frac{25}{4}

= - (\frac{25}{4} + \frac{25}{4})

化简

- (\frac{25}{4} + \frac{25}{4}) : - \frac{25}{2}

= - \frac{25}{2}

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