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Beliebt Rechnen >

integral from 0 to 1 of x(sqrt(x)-x^3)

Lösung

\int_{0}^{1} x (x - x^{3}) d x

Lösung

\frac{1}{5}

+1

Dezimale

0.2

Schritte zur Lösung

\int_{0}^{1} x (x - x^{3}) d x

Wende die partielle Integration an

= [x (\frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{4}}{4}) - \int \frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{4}}{4} d x]_{0}^{1}

\int \frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{4}}{4} d x = \frac{4}{15} x^{\frac{5}{2}} - \frac{x ^{5}}{20}

= [x (\frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{4}}{4}) - (\frac{4}{15} x^{\frac{5}{2}} - \frac{x ^{5}}{20})]_{0}^{1}

Vereinfache

[x (\frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{4}}{4}) - (\frac{4}{15} x^{\frac{5}{2}} - \frac{x ^{5}}{20})]_{0}^{1} : [\frac{1}{5} (- x^{5} + 2 x^{\frac{5}{2}})]_{0}^{1}

= [\frac{1}{5} (- x^{5} + 2 x^{\frac{5}{2}})]_{0}^{1}

Berechne die Grenzen:

\frac{1}{5}

= \frac{1}{5}

Graph

Beliebte Beispiele

integral from 0 to 4 of 3e^t

\int_{0}^{4} 3 e^{t} d t

integral from-2 to 2 of 16^{x/2}

\int_{- 2}^{2} 1 6^{\frac{x}{2}} d x

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

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

integral from-pi to 0 of 1/pi

\int_{- π}^{0} \frac{1}{π}

integral from-2 to 2 of 5t^4

\int_{- 2}^{2} 5 t^{4} d t