integral from-9 to 0 of (1+sqrt(81-x^2))

Lösung

\int_{- 9}^{0} (1 + 81 - x^{2}) d x

9 + \frac{81 π}{4}

Dezimale

72.61725 \dots

Schritte zur Lösung

\int_{- 9}^{0} 1 + 81 - x^{2} d x

Wende die Summenregel an:

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

= \int_{- 9}^{0} 1 d x + \int_{- 9}^{0} 81 - x^{2} d x

\int_{- 9}^{0} 1 d x = 9

\int_{- 9}^{0} 81 - x^{2} d x = \frac{81 π}{4}

= 9 + \frac{81 π}{4}

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