integral from 0 to 1 of x^3sqrt(7+5x^4)

Lösung

\int_{0}^{1} x^{3} 7 + 5 x^{4} d x

\frac{24 3 - 7 7}{30}

Dezimale

0.76829 \dots

Schritte zur Lösung

\int_{0}^{1} x^{3} 7 + 5 x^{4} d x

Wende U-Substitution an

= \int_{7}^{23} \frac{u ^{2}}{10} d u

Entferne die Konstante:

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

= \frac{1}{10} \cdot \int_{7}^{23} u^{2} d u

Wende die Potenzregel an

= \frac{1}{10} [\frac{u ^{3}}{3}]_{7}^{23}

Berechne die Grenzen:

83 - \frac{7 7}{3}

= \frac{1}{10} (83 - \frac{7 7}{3})

Vereinfache

= \frac{24 3 - 7 7}{30}

\int_{0}^{1} (x - 6) e^{x} d x

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