integral from 0 to pi/2 of 1-cos(x)

Lösung

\int_{0}^{\frac{π}{2}} 1 - cos (x) d x

\frac{π}{2} - 1

Dezimale

0.57079 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} 1 - cos (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

= \int_{0}^{\frac{π}{2}} 1 d x - \int_{0}^{\frac{π}{2}} cos (x) d x

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

\int_{0}^{\frac{π}{2}} cos (x) d x = 1

= \frac{π}{2} - 1

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