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

Lösung

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

\frac{2 ( 5 5 - 1 )}{3}

Dezimale

6.78689 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende U-Substitution an

= 2 \cdot \int_{1}^{5} u^{2} d u

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{5 5}{3} - \frac{1}{3}

= 2 (\frac{5 5}{3} - \frac{1}{3})

Vereinfache

= \frac{2 ( 5 5 - 1 )}{3}

\int_{0}^{\frac{1}{2}} t d t

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\int_{0}^{x} (x - t) d t