integral from-4 to 4 of 4(16-x^2)

解

\int_{- 4}^{4} 4 (16 - x^{2}) d x

\frac{1024}{3}

十進法表記

341.33333 \dots

解答ステップ

\int_{- 4}^{4} 4 (16 - x^{2}) d x

定数を除く:

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

= 4 \cdot \int_{- 4}^{4} 16 - 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

= 4 (\int_{- 4}^{4} 16 d x - \int_{- 4}^{4} x^{2} d x)

\int_{- 4}^{4} 16 d x = 128

\int_{- 4}^{4} x^{2} d x = \frac{128}{3}

= 4 (128 - \frac{128}{3})

簡素化

4 (128 - \frac{128}{3}) : \frac{1024}{3}

= \frac{1024}{3}