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

פתרון

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

\frac{9}{2} + \frac{9 π}{4}

סימון עשרוני

11.56858 \dots

צעדי פתרון

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

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

:הפעל את תכונת הליניאריות

= \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}

- \frac{9}{2} + 9 + \frac{9 π}{4}

פשט את:

\frac{9}{2} + \frac{9 π}{4}

= \frac{9}{2} + \frac{9 π}{4}

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