integral from 0 to 1 of sqrt(3x+5)

Lösung

\int_{0}^{1} 3 x + 5 d x

\frac{32 2 - 10 5}{9}

Dezimale

2.54379 \dots

Schritte zur Lösung

\int_{0}^{1} 3 x + 5 d x

Wende U-Substitution an

= \int_{5}^{8} \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_{5}^{8} u d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{8}

Berechne die Grenzen:

\frac{32 2 - 10 5}{3}

= \frac{1}{3} \cdot \frac{32 2 - 10 5}{3}

Vereinfache

= \frac{32 2 - 10 5}{9}

\int_{0}^{t} (t - w) e^{5 w} d w

\int_{0}^{4} e^{x} x^{2} d x

\int_{0}^{2} \frac{4}{5 x + 1} d x

\int_{- 3}^{1} e^{u + 3} d u

\int_{1}^{3} (4 - x^{2}) d x