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受欢迎的微积分 >

integral from 0 to 1 of 1/(sqrt(1+8x))

解答

\int_{0}^{1} \frac{1}{1 + 8 x} d x

解答

\frac{1}{2}

+1

十进制

0.5

求解步骤

\int_{0}^{1} \frac{1}{1 + 8 x} d x

使用换元积分法

= \int_{1}^{9} \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_{1}^{9} \frac{1}{u} d u

使用幂法则

= \frac{1}{8} [2 u^{\frac{1}{2}}]_{1}^{9}

使用根式运算法则:

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

= \frac{1}{8} [2 u]_{1}^{9}

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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\int_{0}^{2} e^{- x^{3}} d x

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