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Beliebt Rechnen >

integral from 0 to 1 of xsqrt(8-x^2)

Lösung

\int_{0}^{1} x 8 - x^{2} d x

Lösung

\frac{16 2 - 7 7}{3}

+1

Dezimale

1.36905 \dots

Schritte zur Lösung

\int_{0}^{1} x 8 - x^{2} d x

Wende U-Substitution an

= \int_{8}^{7} - \frac{u}{2} d u

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

= - \int_{7}^{8} - \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}^{8} u d u)

Wende die Potenzregel an

= - (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{8})

Vereinfache

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{8}

Berechne die Grenzen:

\frac{32 2 - 14 7}{3}

= \frac{1}{2} \cdot \frac{32 2 - 14 7}{3}

Vereinfache

= \frac{16 2 - 7 7}{3}

Graph

Beliebte Beispiele

(1+ln(x)+y/x)dx=(7-ln(x))dy

(1 + ln (x) + \frac{y}{x}) d x = (7 - ln (x)) d y

limit as x approaches-7 of sqrt(1/(x+7))

x \to - 7 lim (\frac{1}{x + 7})

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derivative of ln(e^{6x})

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integral of (1/(sqrt(9-x^2)))

\int (\frac{1}{9 - x ^{2}}) d x