integral from 1 to 2 of (4x^{3/2})

解答

\int_{1}^{2} (4 x^{\frac{3}{2}}) d x

\frac{4 ( 8 \cdot 2 ^{\frac{1}{2}} - 2 )}{5}

十进制

7.45096 \dots

求解步骤

\int_{1}^{2} 4 x^{\frac{3}{2}} d x

提出常数:

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

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

使用幂法则

= 4 [\frac{2}{5} x^{\frac{5}{2}}]_{1}^{2}

带入上下限计算后得:

\frac{8 \cdot 2 ^{\frac{1}{2}}}{5} - \frac{2}{5}

= 4 (\frac{8 \cdot 2 ^{\frac{1}{2}}}{5} - \frac{2}{5})

化简

= \frac{4 ( 8 \cdot 2 ^{\frac{1}{2}} - 2 )}{5}

\frac{d}{d x} (4 x^{3} - x + 3)

\frac{\partial}{\partial x} (8 x^{6 y})

\frac{\partial}{\partial x} (20)

\frac{\partial}{\partial y} (\frac{1}{4} x^{2} + y^{2} - 1)

d er i v a t i v e g (x) = x^{2} + sin (x)