integral from 2 to 3 of sqrt(32x-63)

Lösung

\int_{2}^{3} 32 x - 63 d x

\frac{33 33 - 1}{48}

Dezimale

3.92855 \dots

Schritte zur Lösung

\int_{2}^{3} 32 x - 63 d x

Wende U-Substitution an

= \int_{1}^{33} \frac{u}{32} d u

Entferne die Konstante:

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

= \frac{1}{32} \cdot \int_{1}^{33} u d u

Wende die Potenzregel an

= \frac{1}{32} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{33}

Berechne die Grenzen:

2233 - \frac{2}{3}

= \frac{1}{32} (2233 - \frac{2}{3})

Vereinfache

= \frac{33 33 - 1}{48}

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