integral from 0 to 12 of 98009pi(12-x)

Lösung

\int_{0}^{12} 9800 \cdot 9 π \cdot (12 - x) d x

6350400 π

Dezimale

19950369.98735 \dots

Schritte zur Lösung

\int_{0}^{12} 9800 \cdot 9 π (12 - x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9800 \cdot 9 π \cdot \int_{0}^{12} 12 - x d x

Vereinfache

= 88200 π \cdot \int_{0}^{12} 12 - x 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

= 88200 π (\int_{0}^{12} 12 d x - \int_{0}^{12} x d x)

\int_{0}^{12} 12 d x = 144

\int_{0}^{12} x d x = 72

= 88200 π (144 - 72)

Vereinfache

= 6350400 π

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