integral from 0 to y of 6(y-x)

Lösung

\int_{0}^{y} 6 (y - x) d x

3 y^{2}

Schritte zur Lösung

\int_{0}^{y} 6 (y - x) d x

Entferne die Konstante:

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

= 6 \cdot \int_{0}^{y} y - 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

= 6 (\int_{0}^{y} y d x - \int_{0}^{y} x d x)

\int_{0}^{y} y d x = y^{2}

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

= 6 (y^{2} - \frac{y ^{2}}{2})

Vereinfache

6 (y^{2} - \frac{y ^{2}}{2}) : 3 y^{2}

= 3 y^{2}

\int_{0.25}^{0.5} 20 x^{3} (1 - x) d x

\int_{5}^{11} \frac{1}{x - 2} d x

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\int_{0}^{3} x^{3} - 3 x^{2} d x

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