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

Lösung

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

- 2

Schritte zur Lösung

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

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

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 3 x d x = 6

= \frac{4}{3} + \frac{8}{3} - 6

Vereinfache

\frac{4}{3} + \frac{8}{3} - 6 : - 2

= - 2

\int_{0}^{π} 3 d x

\int_{1}^{0} ln (x) d x

\int_{1}^{4} \frac{1}{( x - 2 ) ^{\frac{3}{2}}} d x

\int_{0}^{1} x \cdot x d x

\int_{1}^{4} \frac{1}{( x + 3 ) ^{2}} d x