integral from 1 to 4 of (sqrt(x)-1)

解答

\int_{1}^{4} (x - 1) d x

\frac{5}{3}

十进制

1.66666 \dots

求解步骤

\int_{1}^{4} x - 1 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_{1}^{4} x d x - \int_{1}^{4} 1 d x

\int_{1}^{4} x d x = \frac{14}{3}

\int_{1}^{4} 1 d x = 3

= \frac{14}{3} - 3

化简

\frac{14}{3} - 3 : \frac{5}{3}

= \frac{5}{3}

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