integral from-2 to 1 of x^3+2x^2-x+2

Lösung

\int_{- 2}^{1} x^{3} + 2 x^{2} - x + 2 d x

\frac{39}{4}

Dezimale

9.75

Schritte zur Lösung

\int_{- 2}^{1} x^{3} + 2 x^{2} - x + 2 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_{- 2}^{1} x^{3} d x + \int_{- 2}^{1} 2 x^{2} d x - \int_{- 2}^{1} x d x + \int_{- 2}^{1} 2 d x

\int_{- 2}^{1} x^{3} d x = - \frac{15}{4}

\int_{- 2}^{1} 2 x^{2} d x = 6

\int_{- 2}^{1} x d x = - \frac{3}{2}

\int_{- 2}^{1} 2 d x = 6

= - \frac{15}{4} + 6 - (- \frac{3}{2}) + 6

Vereinfache

- \frac{15}{4} + 6 - (- \frac{3}{2}) + 6 : \frac{39}{4}

= \frac{39}{4}

\int_{1}^{4} \frac{4}{x} - \frac{x}{4} d x

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

\int_{2}^{3} \frac{2}{x ^{2}} d x

\int_{l n (2)}^{l n (3)} e^{x} d x

\int_{- 7}^{4} ∣ x ∣ d x