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受欢迎的微积分 >

integral from 0 to 2 of 4/(sqrt(5x+3))

解答

\int_{0}^{2} \frac{4}{5 x + 3} d x

解答

\frac{4 ( 2 13 - 2 3 )}{5}

+1

十进制

2.99760 \dots

求解步骤

\int_{0}^{2} \frac{4}{5 x + 3} d x

提出常数:

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

= 4 \cdot \int_{0}^{2} \frac{1}{5 x + 3} d x

使用换元积分法

= 4 \cdot \int_{3}^{13} \frac{1}{5 u} d u

提出常数:

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

= 4 \cdot \frac{1}{5} \cdot \int_{3}^{13} \frac{1}{u} d u

使用幂法则

= 4 \cdot \frac{1}{5} [2 u^{\frac{1}{2}}]_{3}^{13}

化简

4 \cdot \frac{1}{5} [2 u^{\frac{1}{2}}]_{3}^{13} : \frac{4}{5} [2 u]_{3}^{13}

= \frac{4}{5} [2 u]_{3}^{13}

带入上下限计算后得:

213 - 23

= \frac{4}{5} (213 - 23)

化简

= \frac{4 ( 2 13 - 2 3 )}{5}

作图

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