integral from 2 to 3 of sqrt(12-4x)

Lösung

\int_{2}^{3} 12 - 4 x d x

\frac{4}{3}

Dezimale

1.33333 \dots

Schritte zur Lösung

\int_{2}^{3} 12 - 4 x d x

Wende U-Substitution an

= \int_{4}^{0} - \frac{u}{4} d u

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

= - \int_{0}^{4} - \frac{u}{4} d u

Entferne die Konstante:

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

= - (- \frac{1}{4} \cdot \int_{0}^{4} u d u)

Wende die Potenzregel an

= - (- \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{4})

Vereinfache

= \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{4}

Berechne die Grenzen:

\frac{16}{3}

= \frac{1}{4} \cdot \frac{16}{3}

Vereinfache

= \frac{4}{3}

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