integral from 1 to 2 of sqrt(2x-1)

Lösung

\int_{1}^{2} 2 x - 1 d x

\frac{3 3 - 1}{3}

Dezimale

1.39871 \dots

Schritte zur Lösung

\int_{1}^{2} 2 x - 1 d x

Wende U-Substitution an

= \int_{1}^{3} \frac{u}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{1}^{3} u d u

Wende die Potenzregel an

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

Berechne die Grenzen:

23 - \frac{2}{3}

= \frac{1}{2} (23 - \frac{2}{3})

Vereinfache

= \frac{3 3 - 1}{3}

\int_{0}^{1} 9 x^{3} d x

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

\int_{2}^{3} - \frac{4}{x ^{2}} d x

\int_{0}^{1} 1 5^{2 x} d x

\int_{0}^{1} x^{2} 9 - x^{3} d x