integral from 1 to 2 of sqrt(1+9/4 x)

Lösung

\int_{1}^{2} 1 + \frac{9}{4} x d x

\frac{44 11 - 13 26}{27 2}

Dezimale

2.08581 \dots

Schritte zur Lösung

\int_{1}^{2} 1 + \frac{9}{4} x d x

Wende U-Substitution an

= \int_{\frac{13}{4}}^{\frac{11}{2}} \frac{4 u}{9} d u

Entferne die Konstante:

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

= \frac{4}{9} \cdot \int_{\frac{13}{4}}^{\frac{11}{2}} u d u

Wende die Potenzregel an

= \frac{4}{9} [\frac{2}{3} u^{\frac{3}{2}}]_{\frac{13}{4}}^{\frac{11}{2}}

Berechne die Grenzen:

\frac{11 11}{3 2} - \frac{13 13}{12}

= \frac{4}{9} (\frac{11 11}{3 2} - \frac{13 13}{12})

Vereinfache

= \frac{44 11 - 13 26}{27 2}