integral from 2 to 10 of (x^2+36)/(12x)

解答

\int_{2}^{10} \frac{x ^{2} + 36}{12 x} d x

\frac{1}{12} (48 + 36 ln (5))

十进制

8.82831 \dots

求解步骤

\int_{2}^{10} \frac{x ^{2} + 36}{12 x} d x

提出常数:

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

= \frac{1}{12} \cdot \int_{2}^{10} \frac{x ^{2} + 36}{x} d x

乘开

\frac{x ^{2} + 36}{x} : x + \frac{36}{x}

= \frac{1}{12} \cdot \int_{2}^{10} x + \frac{36}{x} d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{12} (\int_{2}^{10} x d x + \int_{2}^{10} \frac{36}{x} d x)

\int_{2}^{10} x d x = 48

\int_{2}^{10} \frac{36}{x} d x = 36 ln (5)

= \frac{1}{12} (48 + 36 ln (5))

x^{^{'''}} - x^{^{''}} - x^{^{'}} + x = 2 e^{- t} + 3

\frac{\partial}{\partial x} (8 x - 2 y - 2)

\frac{\partial}{\partial y} (\frac{y}{z})

\int 20 x sin (5 x^{2} - 3) d x

t an g e n t f (x) = \frac{9}{x ^{2}}, at x = - 1