integral from 4 to 9 of (2x-5)/4

解答

\int_{4}^{9} \frac{2 x - 5}{4} d x

10

求解步骤

\int_{4}^{9} \frac{2 x - 5}{4} d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int_{4}^{9} 2 x - 5 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

= \frac{1}{4} (\int_{4}^{9} 2 x d x - \int_{4}^{9} 5 d x)

\int_{4}^{9} 2 x d x = 65

\int_{4}^{9} 5 d x = 25

= \frac{1}{4} (65 - 25)

化简

\frac{1}{4} (65 - 25) : 10

= 10

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