integral from 3 to 5 of 3x(x+2)

解答

\int_{3}^{5} 3 x (x + 2) d x

146

求解步骤

\int_{3}^{5} 3 x (x + 2) d x

提出常数:

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

= 3 \cdot \int_{3}^{5} x (x + 2) d x

乘开

x (x + 2) : x^{2} + 2 x

= 3 \cdot \int_{3}^{5} x^{2} + 2 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

= 3 (\int_{3}^{5} x^{2} d x + \int_{3}^{5} 2 x d x)

\int_{3}^{5} x^{2} d x = \frac{98}{3}

\int_{3}^{5} 2 x d x = 16

= 3 (\frac{98}{3} + 16)

化简

3 (\frac{98}{3} + 16) : 146

= 146

\int_{0}^{1} x^{- 0.5} d x

\int_{1}^{2} (a x^{3} + \frac{6}{x ^{2}}) d x

\int_{- 1}^{1} x^{2} e^{x} d x

\int_{0}^{1} (x^{17} + 1 7^{x}) d x

\int_{- 4}^{5} ∣ x ∣ d x