integral from 0 to 2 of 2x^2-x^3

Lösung

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

\frac{4}{3}

Dezimale

1.33333 \dots

Schritte zur Lösung

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{0}^{2} 2 x^{2} d x = \frac{16}{3}

\int_{0}^{2} x^{3} d x = 4

= \frac{16}{3} - 4

Vereinfache

\frac{16}{3} - 4 : \frac{4}{3}

= \frac{4}{3}

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

x \to \infty lim (\frac{- 2}{x})

\int 4 sin^{2} (5 x + 3) + 10 x^{\frac{2}{3}} - 1 d x

\frac{d}{d x} (\frac{x + 1}{3 x + 2})

e x p an d 6 x (x^{2} - 5)^{2}