integral from 0 to 3 of tsqrt(4+9t^2)

Lösung

\int_{0}^{3} t 4 + 9 t^{2} d t

\frac{85 85 - 8}{27}

Dezimale

28.72819 \dots

Schritte zur Lösung

\int_{0}^{3} t 4 + 9 t^{2} d t

Wende U-Substitution an

= \int_{4}^{85} \frac{u}{18} d u

Entferne die Konstante:

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

= \frac{1}{18} \cdot \int_{4}^{85} u d u

Wende die Potenzregel an

= \frac{1}{18} [\frac{2}{3} u^{\frac{3}{2}}]_{4}^{85}

Berechne die Grenzen:

\frac{170 85}{3} - \frac{16}{3}

= \frac{1}{18} (\frac{170 85}{3} - \frac{16}{3})

Vereinfache

= \frac{85 85 - 8}{27}

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