integral from 4 to 9 of 2sqrt(x)(10x+3)

解

\int_{4}^{9} 2 x (10 x + 3) d x

1764

解答ステップ

\int_{4}^{9} 2 x (10 x + 3) d x

定数を除く:

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

= 2 \cdot \int_{4}^{9} x (10 x + 3) d x

拡張

x (10 x + 3) : 10 x^{\frac{3}{2}} + 3 x

= 2 \cdot \int_{4}^{9} 10 x^{\frac{3}{2}} + 3 x d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int_{4}^{9} 10 x^{\frac{3}{2}} d x + \int_{4}^{9} 3 x d x)

\int_{4}^{9} 10 x^{\frac{3}{2}} d x = 844

\int_{4}^{9} 3 x d x = 38

= 2 (844 + 38)

簡素化

= 1764