integral from-1 to 0 of sqrt(1-3x)

Lösung

\int_{- 1}^{0} 1 - 3 x d x

\frac{14}{9}

Dezimale

1.55555 \dots

Schritte zur Lösung

\int_{- 1}^{0} 1 - 3 x d x

Wende U-Substitution an

= \int_{4}^{1} - \frac{u}{3} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{4} - \frac{u}{3} d u

Entferne die Konstante:

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

= - (- \frac{1}{3} \cdot \int_{1}^{4} u d u)

Wende die Potenzregel an

= - (- \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{4})

Vereinfache

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{4}

Berechne die Grenzen:

\frac{14}{3}

= \frac{1}{3} \cdot \frac{14}{3}

Vereinfache

= \frac{14}{9}

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