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

Lösung

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

\frac{10}{3}

Dezimale

3.33333 \dots

Schritte zur Lösung

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

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

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

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

= - 4 + \frac{16}{3} + 2

Vereinfache

- 4 + \frac{16}{3} + 2 : \frac{10}{3}

= \frac{10}{3}

\int_{0}^{9} \frac{x}{36 + 5 x} d x

\int_{2}^{4} (1 + x) d x

\int_{- \frac{π}{3}}^{0} (sin (x)) d x

\int_{1}^{5} \frac{1}{( 10 - x ) ^{2}} d x

\int_{- 5}^{10} 5 - ∣ x ∣ d x