integral from 0 to 1 of pi(1-x)

Lösung

\int_{0}^{1} π (1 - x) d x

\frac{π}{2}

Dezimale

1.57079 \dots

Schritte zur Lösung

\int_{0}^{1} π (1 - x) d x

Entferne die Konstante:

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

= π \cdot \int_{0}^{1} 1 - 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

= π (\int_{0}^{1} 1 d x - \int_{0}^{1} x d x)

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

\int_{0}^{1} x d x = \frac{1}{2}

= π (1 - \frac{1}{2})

Vereinfache

π (1 - \frac{1}{2}) : \frac{π}{2}

= \frac{π}{2}

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