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受欢迎的微积分 >

integral from 3 to 11 of 1/(sqrt(2x+3))

解答

\int_{3}^{11} \frac{1}{2 x + 3} d x

解答

2

求解步骤

\int_{3}^{11} \frac{1}{2 x + 3} d x

使用换元积分法

= \int_{9}^{25} \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_{9}^{25} \frac{1}{u} d u

使用幂法则

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{9}^{25}

使用根式运算法则:

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

= \frac{1}{2} [2 u]_{9}^{25}

带入上下限计算后得:

4

= \frac{1}{2} \cdot 4

化简

= 2

作图

流行的例子

t a y l or x^{\frac{9}{6}}

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d er i v a t i v e f (t) = 9 t - 2 t^{2}

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limit as x approaches 0 of 1/(sqrt(1-x))

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