integral from 0 to 4 of sqrt(x)(3-5x)

解

\int_{0}^{4} x (3 - 5 x) d x

- 48

解答ステップ

\int_{0}^{4} x (3 - 5 x) d x

拡張

x (3 - 5 x) : 3 x - 5 x^{\frac{3}{2}}

= \int_{0}^{4} 3 x - 5 x^{\frac{3}{2}} 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

= \int_{0}^{4} 3 x d x - \int_{0}^{4} 5 x^{\frac{3}{2}} d x

\int_{0}^{4} 3 x d x = 16

\int_{0}^{4} 5 x^{\frac{3}{2}} d x = 64

= 16 - 64

簡素化

= - 48