integral from 0 to 2 of ysqrt(2+4y^2)

Lösung

\int_{0}^{2} y 2 + 4 y^{2} d y

\frac{13 2}{3}

Dezimale

6.12825 \dots

Schritte zur Lösung

\int_{0}^{2} y 2 + 4 y^{2} d y

Wende U-Substitution an

= \int_{2}^{18} \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_{2}^{18} u d u

Wende die Potenzregel an

= \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{18}

Berechne die Grenzen:

362 - \frac{4 2}{3}

= \frac{1}{8} (362 - \frac{4 2}{3})

Vereinfache

= \frac{13 2}{3}

\int_{8}^{16} (x + \frac{1}{x}) d x

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