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

Lösung

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

\frac{9}{2}

Dezimale

4.5

Schritte zur Lösung

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

Vereinfache

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

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

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

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

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

Vereinfache

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

= \frac{9}{2}

\int_{1}^{4} (x^{2} + 5 x - 12) d x

\int_{- 4}^{6} 12 + x - \frac{1}{2} x^{2} d x

\int_{0}^{1} \frac{1}{( 1 - x ) ^{\frac{2}{3}}} d x

\int_{0}^{π} cos^{3} (θ) sin (θ) d θ

\int_{0}^{1} (x - \frac{3}{4})^{2} 3 x^{2} d x