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

Lösung

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

\frac{52}{9}

Dezimale

5.77777 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{9} \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_{1}^{9} u d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{9}

Berechne die Grenzen:

\frac{52}{3}

= \frac{1}{3} \cdot \frac{52}{3}

Vereinfache

= \frac{52}{9}

\int_{2}^{x} \frac{1}{1 + t ^{2}} d t

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