integral from 1 to 2 of (7x+x^2)

解答

\int_{1}^{2} (7 x + x^{2}) d x

\frac{77}{6}

十进制

12.83333 \dots

求解步骤

\int_{1}^{2} 7 x + x^{2} 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

= \int_{1}^{2} 7 x d x + \int_{1}^{2} x^{2} d x

\int_{1}^{2} 7 x d x = \frac{21}{2}

\int_{1}^{2} x^{2} d x = \frac{7}{3}

= \frac{21}{2} + \frac{7}{3}

化简

\frac{21}{2} + \frac{7}{3} : \frac{77}{6}

= \frac{77}{6}

d er i v a t i v e cos (2^{x})

x^{2} y \frac{d y}{d x} = e^{y}

x \to 2 - lim (\frac{x - 2}{∣ x - 2 ∣})

y^{^{'}} = \frac{( 3 x ^{2} - e ^{x} )}{2 y - 5}

y^{^{''}} + 11 y^{^{'}} + 30 y = 0, y (0) = 1, y^{^{'}} (0) = 0