integral from 8 to 10 of x(x^2-64)^2

解

\int_{8}^{10} x (x^{2} - 64)^{2} d x

7776

解答ステップ

\int_{8}^{10} x (x^{2} - 64)^{2} d x

拡張

x (x^{2} - 64)^{2} : x^{5} - 128 x^{3} + 4096 x

= \int_{8}^{10} x^{5} - 128 x^{3} + 4096 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

= \int_{8}^{10} x^{5} d x - \int_{8}^{10} 128 x^{3} d x + \int_{8}^{10} 4096 x d x

\int_{8}^{10} x^{5} d x = 122976

\int_{8}^{10} 128 x^{3} d x = 188928

\int_{8}^{10} 4096 x d x = 73728

= 122976 - 188928 + 73728

簡素化

= 7776