integral from 3 to 5 of (x^3)/8

解答

\int_{3}^{5} \frac{x ^{3}}{8} d x

17

求解步骤

\int_{3}^{5} \frac{x ^{3}}{8} d x

提出常数:

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

= \frac{1}{8} \cdot \int_{3}^{5} x^{3} d x

使用幂法则

= \frac{1}{8} [\frac{x ^{4}}{4}]_{3}^{5}

带入上下限计算后得:

136

= \frac{1}{8} \cdot 136

化简

= 17

\int_{0}^{2 π} sin (2 x) sin (x) d x

n = 0 \sum \infty (\frac{- 1}{2})^{n}

t an g e n t f (x) = 4 x (x^{2} - 4 x + 5)^{9}, at x = 2

\frac{d}{d x} (9 e^{- 4 x})

y^{3} \frac{d y}{d x} + x^{3} = 0