integral from 0 to 1 of x^7sqrt(1+3x^8)

Lösung

\int_{0}^{1} x^{7} 1 + 3 x^{8} d x

\frac{7}{36}

Dezimale

0.19444 \dots

Schritte zur Lösung

\int_{0}^{1} x^{7} 1 + 3 x^{8} d x

Wende U-Substitution an

= \int_{1}^{4} \frac{u}{24} d u

Entferne die Konstante:

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

= \frac{1}{24} \cdot \int_{1}^{4} u d u

Wende die Potenzregel an

= \frac{1}{24} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{4}

Berechne die Grenzen:

\frac{14}{3}

= \frac{1}{24} \cdot \frac{14}{3}

Vereinfache

= \frac{7}{36}

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

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