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Beliebt Rechnen >

integral from 0 to 3 of xsqrt(16-x^2)

Lösung

\int_{0}^{3} x 16 - x^{2} d x

Lösung

\frac{64 - 7 7}{3}

+1

Dezimale

15.15991 \dots

Schritte zur Lösung

\int_{0}^{3} x 16 - x^{2} d x

Wende U-Substitution an

= \int_{16}^{7} - \frac{u}{2} d u

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

= - \int_{7}^{16} - \frac{u}{2} d u

Entferne die Konstante:

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

= - (- \frac{1}{2} \cdot \int_{7}^{16} u d u)

Wende die Potenzregel an

= - (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{16})

Vereinfache

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{16}

Berechne die Grenzen:

\frac{128}{3} - \frac{14 7}{3}

= \frac{1}{2} (\frac{128}{3} - \frac{14 7}{3})

Vereinfache

= \frac{64 - 7 7}{3}

Graph

Beliebte Beispiele

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integral of 3xsqrt(2x^2+1)

\int 3 x 2 x^{2} + 1 d x