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Beliebt Rechnen >

integral from 0 to 1/2 of xsqrt(1-4x^2)

Lösung

\int_{0}^{\frac{1}{2}} x 1 - 4 x^{2} d x

Lösung

\frac{1}{12}

+1

Dezimale

0.08333 \dots

Schritte zur Lösung

\int_{0}^{\frac{1}{2}} x 1 - 4 x^{2} d x

Wende U-Substitution an

= \int_{1}^{0} - \frac{u}{8} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{1} - \frac{u}{8} d u

Entferne die Konstante:

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

= - (- \frac{1}{8} \cdot \int_{0}^{1} u d u)

Wende die Potenzregel an

= - (- \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{1})

Vereinfache

= \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{1}

Berechne die Grenzen:

\frac{2}{3}

= \frac{1}{8} \cdot \frac{2}{3}

Vereinfache

= \frac{1}{12}

Graph

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