integral from 0 to x of (36-x^2)/(144)

解

\int_{0}^{x} \frac{36 - x ^{2}}{144} d x

\frac{1}{144} (36 x - \frac{x ^{3}}{3})

解答ステップ

\int_{0}^{x} \frac{36 - x ^{2}}{144} d x

定数を除く:

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

= \frac{1}{144} \cdot \int_{0}^{x} 36 - x^{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

= \frac{1}{144} (\int_{0}^{x} 36 d x - \int_{0}^{x} x^{2} d x)

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

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

= \frac{1}{144} (36 x - \frac{x ^{3}}{3})