integral from 0 to 1 of x+sqrt(1-x^2)

Lösung

\int_{0}^{1} x + 1 - x^{2} d x

\frac{1}{2} + \frac{π}{4}

Dezimale

1.28539 \dots

Schritte zur Lösung

\int_{0}^{1} x + 1 - 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_{0}^{1} x d x + \int_{0}^{1} 1 - x^{2} d x

\int_{0}^{1} x d x = \frac{1}{2}

\int_{0}^{1} 1 - x^{2} d x = \frac{π}{4}

= \frac{1}{2} + \frac{π}{4}