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Beliebt Rechnen >

integral from 0 to 1.5 of (-4x+6)^{3/2}

Lösung

\int_{0}^{1.5} (- 4 x + 6)^{\frac{3}{2}} d x

Lösung

\frac{18 \cdot 6 ^{\frac{1}{2}}}{5}

+1

Dezimale

8.81816 \dots

Schritte zur Lösung

\int_{0}^{1.5} (- 4 x + 6)^{\frac{3}{2}} d x

Wende U-Substitution an

= \int_{6}^{0} - \frac{u ^{\frac{3}{2}}}{4} d u

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

= - \int_{0}^{6} - \frac{u ^{\frac{3}{2}}}{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}^{6} u^{\frac{3}{2}} d u)

Wende die Potenzregel an

= - (- \frac{1}{4} [\frac{2}{5} u^{\frac{5}{2}}]_{0}^{6})

Vereinfache

= \frac{1}{4} [\frac{2}{5} u^{\frac{5}{2}}]_{0}^{6}

Berechne die Grenzen:

\frac{72 \cdot 6 ^{\frac{1}{2}}}{5}

= \frac{1}{4} \cdot \frac{72 \cdot 6 ^{\frac{1}{2}}}{5}

Vereinfache

= \frac{18 \cdot 6 ^{\frac{1}{2}}}{5}

Graph

Beliebte Beispiele

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\int_{1}^{e^{2}} ln (x) d x

integral from-5 to 0 of x^3

\int_{- 5}^{0} x^{3} d x

integral from 0 to 4 of (3x^2+x-8)

\int_{0}^{4} (3 x^{2} + x - 8) d x