integral from 0 to 3 of xsqrt(1+4x^2)

Lösung

\int_{0}^{3} x 1 + 4 x^{2} d x

\frac{37 37 - 1}{12}

Dezimale

18.67185 \dots

Schritte zur Lösung

\int_{0}^{3} x 1 + 4 x^{2} d x

Wende U-Substitution an

= \int_{1}^{37} \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_{1}^{37} u d u

Wende die Potenzregel an

= \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{37}

Berechne die Grenzen:

\frac{74 37}{3} - \frac{2}{3}

= \frac{1}{8} (\frac{74 37}{3} - \frac{2}{3})

Vereinfache

= \frac{37 37 - 1}{12}