integral from 1 to 5 of sqrt(3x+1)

Lösung

\int_{1}^{5} 3 x + 1 d x

\frac{112}{9}

Dezimale

12.44444 \dots

Schritte zur Lösung

\int_{1}^{5} 3 x + 1 d x

Wende U-Substitution an

= \int_{4}^{16} \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_{4}^{16} u d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{4}^{16}

Berechne die Grenzen:

\frac{112}{3}

= \frac{1}{3} \cdot \frac{112}{3}

Vereinfache

= \frac{112}{9}

\int_{0}^{\frac{15}{16}} 1 + 16 x d x

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