integral from 0 to 2 of x^2(8-x^3)

Lösung

\int_{0}^{2} x^{2} (8 - x^{3}) d x

\frac{32}{3}

Dezimale

10.66666 \dots

Schritte zur Lösung

\int_{0}^{2} x^{2} (8 - x^{3}) d x

Wende die partielle Integration an

= [\frac{1}{3} x^{3} (8 - x^{3}) - \int - x^{5} d x]_{0}^{2}

\int - x^{5} d x = - \frac{x ^{6}}{6}

= [\frac{1}{3} x^{3} (8 - x^{3}) - (- \frac{x ^{6}}{6})]_{0}^{2}

Vereinfache

[\frac{1}{3} x^{3} (8 - x^{3}) - (- \frac{x ^{6}}{6})]_{0}^{2} : [\frac{1}{6} (16 x^{3} - x^{6})]_{0}^{2}

= [\frac{1}{6} (16 x^{3} - x^{6})]_{0}^{2}

Berechne die Grenzen:

\frac{32}{3}

= \frac{32}{3}

\int_{0}^{x} (3 + sin (t)) d t

\int_{0}^{3} \frac{1}{96} y^{3} e^{- \frac{y}{2}} d y

\int_{0}^{0.9} \frac{cos ( x ) - 1}{x} d x

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

\int_{0}^{4} x - \frac{x ^{2}}{8} d x