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Beliebt Rechnen >

integral from 0 to 1 of sqrt(1+36x)

Lösung

\int_{0}^{1} 1 + 36 x d x

Lösung

\frac{37 37 - 1}{54}

+1

Dezimale

4.14930 \dots

Schritte zur Lösung

\int_{0}^{1} 1 + 36 x d x

Wende U-Substitution an

= \int_{1}^{37} \frac{u}{36} d u

Entferne die Konstante:

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

= \frac{1}{36} \cdot \int_{1}^{37} u d u

Wende die Potenzregel an

= \frac{1}{36} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{37}

Berechne die Grenzen:

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

= \frac{1}{36} (\frac{74 37}{3} - \frac{2}{3})

Vereinfache

= \frac{37 37 - 1}{54}

Graph

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