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Beliebt Rechnen >

integral from 0 to 2 of (15sqrt(4x+1))

Lösung

\int_{0}^{2} (15 4 x + 1) d x

Lösung

65

Schritte zur Lösung

\int_{0}^{2} 15 4 x + 1 d x

Entferne die Konstante:

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

= 15 \cdot \int_{0}^{2} 4 x + 1 d x

Wende U-Substitution an

= 15 \cdot \int_{1}^{9} \frac{u}{4} d u

Entferne die Konstante:

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

= 15 \cdot \frac{1}{4} \cdot \int_{1}^{9} u d u

Wende die Potenzregel an

= 15 \cdot \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{9}

Vereinfache

15 \cdot \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{9} : \frac{15}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{9}

= \frac{15}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{9}

Berechne die Grenzen:

\frac{52}{3}

= \frac{15}{4} \cdot \frac{52}{3}

Vereinfache

= 65

Graph

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