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

Lösung

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

\frac{1}{3} + \frac{π}{2}

Dezimale

1.90412 \dots

Schritte zur Lösung

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

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

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

= \frac{π}{2} + 1 - \frac{2}{3}

Vereinfache

\frac{π}{2} + 1 - \frac{2}{3} : \frac{1}{3} + \frac{π}{2}

= \frac{1}{3} + \frac{π}{2}