integral from 0 to 2 of |2x-3|

解答

\int_{0}^{2} ∣ 2 x - 3 ∣ d x

\frac{5}{2}

十进制

2.5

求解步骤

\int_{0}^{2} ∣ 2 x - 3 ∣ d x

拿掉绝对值

= \int_{0}^{\frac{3}{2}} - 2 x + 3 d x + \int_{\frac{3}{2}}^{2} 2 x - 3 d x

\int_{0}^{\frac{3}{2}} - 2 x + 3 d x = \frac{9}{4}

\int_{\frac{3}{2}}^{2} 2 x - 3 d x = \frac{1}{4}

= \frac{9}{4} + \frac{1}{4}

化简

\frac{9}{4} + \frac{1}{4} : \frac{5}{2}

= \frac{5}{2}

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