integral from-1 to 2 of (4-x^2)-(2-x)

Lösung

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

\frac{9}{2}

Dezimale

4.5

Schritte zur Lösung

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

Vereinfache

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

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

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

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

= - 3 + \frac{3}{2} + 6

Vereinfache

- 3 + \frac{3}{2} + 6 : \frac{9}{2}

= \frac{9}{2}

\int_{1}^{e} x^{3} ln (3 x) d x

\int_{- 1}^{1} t (7 - t)^{2} d t

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

\int_{3}^{4} x^{- 3} d x

\int_{2}^{7} x^{3} d x