integral from 0 to 1 of x^2sqrt(x^3+5)

Lösung

\int_{0}^{1} x^{2} x^{3} + 5 d x

\frac{12 6 - 10 5}{9}

Dezimale

0.78146 \dots

Schritte zur Lösung

\int_{0}^{1} x^{2} x^{3} + 5 d x

Wende U-Substitution an

= \int_{5}^{6} \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}^{6} u d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{6}

Berechne die Grenzen:

46 - \frac{10 5}{3}

= \frac{1}{3} (46 - \frac{10 5}{3})

Vereinfache

= \frac{12 6 - 10 5}{9}

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

\int_{y^{2}}^{y} \frac{x}{y} d x

\int_{0}^{2 π} ∣ sin (2 x) ∣ d x

\int_{0}^{1} (6 x^{2} + \frac{15}{2} x^{3}) d x

\int_{0}^{1} x cosh (2 x) d x