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受欢迎的微积分 >

integral from 3 to 6 of 1/(sqrt(8x+1))

解答

\int_{3}^{6} \frac{1}{8 x + 1} d x

解答

\frac{1}{2}

+1

十进制

0.5

求解步骤

\int_{3}^{6} \frac{1}{8 x + 1} d x

使用换元积分法

= \int_{25}^{49} \frac{1}{8 u} d u

提出常数:

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

= \frac{1}{8} \cdot \int_{25}^{49} \frac{1}{u} d u

使用幂法则

= \frac{1}{8} [2 u^{\frac{1}{2}}]_{25}^{49}

使用根式运算法则:

a^{\frac{1}{n}} = n a

= \frac{1}{8} [2 u]_{25}^{49}

带入上下限计算后得:

4

= \frac{1}{8} \cdot 4

化简

= \frac{1}{2}

作图

流行的例子

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