integral from-1 to 1 of 1-y^2

Lösung

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

\frac{4}{3}

Dezimale

1.33333 \dots

Schritte zur Lösung

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

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

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

= 2 - \frac{2}{3}

Vereinfache

2 - \frac{2}{3} : \frac{4}{3}

= \frac{4}{3}

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