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Beliebt Rechnen >

integral from 0 to 1 of sqrt(t^4+t^2)

Lösung

\int_{0}^{1} t^{4} + t^{2} d t

Lösung

\frac{2 2 - 1}{3}

+1

Dezimale

0.60947 \dots

Schritte zur Lösung

\int_{0}^{1} t^{4} + t^{2} d t

Vereinfache

t^{4} + t^{2} : t^{2} t^{2} + 1

= \int_{0}^{1} t^{2} t^{2} + 1 d t

t^{2} = (t),

angenommen

t \geq 0

= \int_{0}^{1} t t^{2} + 1 d t

Wende U-Substitution an

= \int_{1}^{2} u^{2} d u

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{2 2}{3} - \frac{1}{3}

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

Vereinfache

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

Graph

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