integral from-1 to 0 of x^2(x+1)^{1/2}

Lösung

\int_{- 1}^{0} x^{2} (x + 1)^{\frac{1}{2}} d x

\frac{16}{105}

Dezimale

0.15238 \dots

Schritte zur Lösung

\int_{- 1}^{0} x^{2} (x + 1)^{\frac{1}{2}} d x

Wende die partielle Integration an

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

\int \frac{4}{3} x (x + 1)^{\frac{3}{2}} d x = \frac{4}{3} (\frac{2}{5} x (x + 1)^{\frac{5}{2}} - \frac{4}{35} (x + 1)^{\frac{7}{2}})

= [\frac{2}{3} x^{2} (x + 1)^{\frac{3}{2}} - \frac{4}{3} (\frac{2}{5} x (x + 1)^{\frac{5}{2}} - \frac{4}{35} (x + 1)^{\frac{7}{2}})]_{- 1}^{0}

Berechne die Grenzen:

\frac{16}{105}

= \frac{16}{105}

\int_{- π}^{0} x^{2} cos (n x) d x

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