integral from-3 to 0 of x+3+sqrt(9-x^2)

解

\int_{- 3}^{0} x + 3 + 9 - x^{2} d x

\frac{9}{2} + \frac{9 π}{4}

十進法表記

11.56858 \dots

解答ステップ

\int_{- 3}^{0} x + 3 + 9 - 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}^{0} x d x + \int_{- 3}^{0} 3 d x + \int_{- 3}^{0} 9 - x^{2} d x

\int_{- 3}^{0} x d x = - \frac{9}{2}

\int_{- 3}^{0} 3 d x = 9

\int_{- 3}^{0} 9 - x^{2} d x = \frac{9 π}{4}

= - \frac{9}{2} + 9 + \frac{9 π}{4}

簡素化

- \frac{9}{2} + 9 + \frac{9 π}{4} : \frac{9}{2} + \frac{9 π}{4}

= \frac{9}{2} + \frac{9 π}{4}