integral from 0 to 3 of x(x-2k)

解答

\int_{0}^{3} x (x - 2 k) d x

9 - 9 k

求解步骤

\int_{0}^{3} x (x - 2 k) d x

乘开

x (x - 2 k) : x^{2} - 2 k x

= \int_{0}^{3} x^{2} - 2 k 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

= \int_{0}^{3} x^{2} d x - \int_{0}^{3} 2 k x d x

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} 2 k x d x = 9 k

= 9 - 9 k

\int_{0}^{2} x (\frac{x}{2}) d x

\int_{1}^{5} \frac{2}{t} d t

\int_{- a}^{a} ∣ a + 3 t ∣ d t

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\int_{0}^{3} π (x^{2})^{2} d x