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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{80 10 - 13 13}{27}

+1

Dezimale

7.63370 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{\frac{13}{4}}^{10} \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}}^{10} u d u

Wende die Potenzregel an

= \frac{4}{9} [\frac{2}{3} u^{\frac{3}{2}}]_{\frac{13}{4}}^{10}

Berechne die Grenzen:

\frac{20 10}{3} - \frac{13 13}{12}

= \frac{4}{9} (\frac{20 10}{3} - \frac{13 13}{12})

Vereinfache

= \frac{80 10 - 13 13}{27}

Graph

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