integral from 20 to 30 of (3x+4)^2

解答

\int_{20}^{30} (3 x + 4)^{2} d x

63160

求解步骤

\int_{20}^{30} (3 x + 4)^{2} d x

乘开

(3 x + 4)^{2} : 9 x^{2} + 24 x + 16

= \int_{20}^{30} 9 x^{2} + 24 x + 16 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_{20}^{30} 9 x^{2} d x + \int_{20}^{30} 24 x d x + \int_{20}^{30} 16 d x

\int_{20}^{30} 9 x^{2} d x = 57000

\int_{20}^{30} 24 x d x = 6000

\int_{20}^{30} 16 d x = 160

= 57000 + 6000 + 160

化简

= 63160

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