integral from 0 to 1 of xsqrt(4x^2+5)

Lösung

\int_{0}^{1} x 4 x^{2} + 5 d x

\frac{27 - 5 5}{12}

Dezimale

1.31830 \dots

Schritte zur Lösung

\int_{0}^{1} x 4 x^{2} + 5 d x

Wende U-Substitution an

= \int_{5}^{9} \frac{u}{8} d u

Entferne die Konstante:

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

= \frac{1}{8} \cdot \int_{5}^{9} u d u

Wende die Potenzregel an

= \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{9}

Berechne die Grenzen:

18 - \frac{10 5}{3}

= \frac{1}{8} (18 - \frac{10 5}{3})

Vereinfache

= \frac{27 - 5 5}{12}

\int_{x^{4}}^{x^{7}} (2 t - 1)^{3} d t

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\int_{0}^{1} x^{14} + 1 4^{x} d x

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