integral from-5 to 5 of (5+sqrt(25-x^2))

Lösung

\int_{- 5}^{5} (5 + 25 - x^{2}) d x

50 + \frac{25 π}{2}

Dezimale

89.26990 \dots

Schritte zur Lösung

\int_{- 5}^{5} 5 + 25 - 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_{- 5}^{5} 5 d x + \int_{- 5}^{5} 25 - x^{2} d x

\int_{- 5}^{5} 5 d x = 50

\int_{- 5}^{5} 25 - x^{2} d x = \frac{25 π}{2}

= 50 + \frac{25 π}{2}

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