integral from 0 to 6 of (x-6)^2

解答

\int_{0}^{6} (x - 6)^{2} d x

72

求解步骤

\int_{0}^{6} (x - 6)^{2} d x

乘开

(x - 6)^{2} : x^{2} - 12 x + 36

= \int_{0}^{6} x^{2} - 12 x + 36 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}^{6} x^{2} d x - \int_{0}^{6} 12 x d x + \int_{0}^{6} 36 d x

\int_{0}^{6} x^{2} d x = 72

\int_{0}^{6} 12 x d x = 216

\int_{0}^{6} 36 d x = 216

= 72 - 216 + 216

化简

= 72

\int_{0}^{4} (\frac{x}{1 + 2 x}) d x

\int_{0}^{21} - 117 x + 23273 d x

\int_{- π}^{5 π} cos^{2} (x) d x

\int_{0}^{- \infty} e^{- x^{2}} d x

\int_{1}^{4} x^{2} - x - 6 d x