integral from 0 to 1 of xsqrt(56x^2+25)

Lösung

\int_{0}^{1} x 56 x^{2} + 25 d x

\frac{151}{42}

Dezimale

3.59523 \dots

Schritte zur Lösung

\int_{0}^{1} x 56 x^{2} + 25 d x

Wende U-Substitution an

= \int_{25}^{81} \frac{u}{112} d u

Entferne die Konstante:

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

= \frac{1}{112} \cdot \int_{25}^{81} u d u

Wende die Potenzregel an

= \frac{1}{112} [\frac{2}{3} u^{\frac{3}{2}}]_{25}^{81}

Berechne die Grenzen:

\frac{1208}{3}

= \frac{1}{112} \cdot \frac{1208}{3}

Vereinfache

= \frac{151}{42}

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