integral from 100 to s of 1/(0.2s)

解答

\int_{100}^{s} \frac{1}{0.2 s} d s

5 (ln ∣ s ∣ - 2 ln (10))

求解步骤

\int_{100}^{s} \frac{1}{0.2 s} d s

提出常数:

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

= \frac{1}{0.2} \cdot \int_{100}^{s} \frac{1}{s} d s

化简

= 5 \cdot \int_{100}^{s} \frac{1}{s} d s

使用积分常见定则:

\int \frac{1}{s} d s = ln (∣ s ∣)

= 5 [ln ∣ s ∣]_{100}^{s}

带入上下限计算后得:

ln ∣ s ∣ - 2 ln (10)

= 5 (ln ∣ s ∣ - 2 ln (10))

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