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受欢迎的微积分 >

integral from 0 to 1 of 1/(sqrt(3-2x))

解答

\int_{0}^{1} \frac{1}{3 - 2 x} d x

解答

3 - 1

+1

十进制

0.73205 \dots

求解步骤

\int_{0}^{1} \frac{1}{3 - 2 x} d x

使用换元积分法

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

提出常数:

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

= - (- \frac{1}{2} \cdot \int_{1}^{3} \frac{1}{u} d u)

使用幂法则

= - (- \frac{1}{2} [2 u^{\frac{1}{2}}]_{1}^{3})

化简

- (- \frac{1}{2} [2 u^{\frac{1}{2}}]_{1}^{3}) : \frac{1}{2} [2 u]_{1}^{3}

= \frac{1}{2} [2 u]_{1}^{3}

带入上下限计算后得:

23 - 2

= \frac{1}{2} (23 - 2)

化简

= 3 - 1

作图

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