integral from 1 to 2 of (2-1/2 x)^2

解

\int_{1}^{2} (2 - \frac{1}{2} x)^{2} d x

\frac{19}{12}

十進法表記

1.58333 \dots

解答ステップ

\int_{1}^{2} (2 - \frac{1}{2} x)^{2} d x

簡素化

(2 - \frac{1}{2} x)^{2} : 4 - 2 x + \frac{1}{4} x^{2}

= \int_{1}^{2} 4 - 2 x + \frac{1}{4} 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

= \int_{1}^{2} 4 d x - \int_{1}^{2} 2 x d x + \int_{1}^{2} \frac{1}{4} x^{2} d x

\int_{1}^{2} 4 d x = 4

\int_{1}^{2} 2 x d x = 3

\int_{1}^{2} \frac{1}{4} x^{2} d x = \frac{7}{12}

= 4 - 3 + \frac{7}{12}

簡素化

4 - 3 + \frac{7}{12} : \frac{19}{12}

= \frac{19}{12}