integral from 0 to 1 of 1-y^2

Lösung

\int_{0}^{1} 1 - y^{2} d y

\frac{2}{3}

Dezimale

0.66666 \dots

Schritte zur Lösung

\int_{0}^{1} 1 - y^{2} d y

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}^{1} 1 d y - \int_{0}^{1} y^{2} d y

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

\int_{0}^{1} y^{2} d y = \frac{1}{3}

= 1 - \frac{1}{3}

Vereinfache

1 - \frac{1}{3} : \frac{2}{3}

= \frac{2}{3}

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