integral from 3 to 8 of (x^3-pix^2)

解

\int_{3}^{8} (x^{3} - π x^{2}) d x

\frac{4015}{4} - \frac{485 π}{3}

十進法表記

495.85918 \dots

解答ステップ

\int_{3}^{8} x^{3} - π 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_{3}^{8} x^{3} d x - \int_{3}^{8} π x^{2} d x

\int_{3}^{8} x^{3} d x = \frac{4015}{4}

\int_{3}^{8} π x^{2} d x = \frac{485 π}{3}

= \frac{4015}{4} - \frac{485 π}{3}