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

Lösung

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

\frac{2}{9}

Dezimale

0.22222 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{1} \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_{0}^{1} u d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{1}

Berechne die Grenzen:

\frac{2}{3}

= \frac{1}{3} \cdot \frac{2}{3}

Vereinfache

= \frac{2}{9}

\int_{0}^{\frac{π}{6}} sin^{3} (x) d x

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

\int_{- π}^{π} cos (m x) cos (n x) d x

\int_{0}^{t} t e^{t - t} d t