integral from 3 to 7 of (x+4)^2

解

\int_{3}^{7} (x + 4)^{2} d x

\frac{988}{3}

十進法表記

329.33333 \dots

解答ステップ

\int_{3}^{7} (x + 4)^{2} d x

拡張

(x + 4)^{2} : x^{2} + 8 x + 16

= \int_{3}^{7} x^{2} + 8 x + 16 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_{3}^{7} x^{2} d x + \int_{3}^{7} 8 x d x + \int_{3}^{7} 16 d x

\int_{3}^{7} x^{2} d x = \frac{316}{3}

\int_{3}^{7} 8 x d x = 160

\int_{3}^{7} 16 d x = 64

= \frac{316}{3} + 160 + 64

簡素化

\frac{316}{3} + 160 + 64 : \frac{988}{3}

= \frac{988}{3}