integral from 0 to 3 of 3sqrt(8x+1)

Lösung

\int_{0}^{3} 3 8 x + 1 d x

31

Schritte zur Lösung

\int_{0}^{3} 3 8 x + 1 d x

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{3} 8 x + 1 d x

Wende U-Substitution an

= 3 \cdot \int_{1}^{25} \frac{u}{8} d u

Entferne die Konstante:

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

= 3 \cdot \frac{1}{8} \cdot \int_{1}^{25} u d u

Wende die Potenzregel an

= 3 \cdot \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25}

Vereinfache

3 \cdot \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25} : \frac{3}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25}

= \frac{3}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25}

Berechne die Grenzen:

\frac{248}{3}

= \frac{3}{8} \cdot \frac{248}{3}

Vereinfache

= 31

\int_{4}^{6} x^{2} d x

\int_{0}^{4} x ln (5 - x) d x

\int_{0}^{5} x e^{5 x} d x

\int_{1}^{5} (2 x + 1) d x

\int_{- 1}^{0} - 20 x e^{- x} d x