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受欢迎的微积分 >

integral from 6 to 8 of (50x)/(x^2+2)

解答

\int_{6}^{8} \frac{50 x}{x ^{2} + 2} d x

解答

25 ln (\frac{33}{19})

+1

十进制

13.80171 \dots

求解步骤

\int_{6}^{8} \frac{50 x}{x ^{2} + 2} d x

提出常数:

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

= 50 \cdot \int_{6}^{8} \frac{x}{x ^{2} + 2} d x

使用换元积分法

= 50 \cdot \int_{38}^{66} \frac{1}{2 u} d u

提出常数:

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

= 50 \cdot \frac{1}{2} \cdot \int_{38}^{66} \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 50 \cdot \frac{1}{2} [ln ∣ u ∣]_{38}^{66}

化简

50 \cdot \frac{1}{2} [ln ∣ u ∣]_{38}^{66} : 25 [ln ∣ u ∣]_{38}^{66}

= 25 [ln ∣ u ∣]_{38}^{66}

带入上下限计算后得:

ln (66) - ln (38)

= 25 (ln (66) - ln (38))

化简

= 25 ln (\frac{33}{19})

作图

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