integral from 0 to 1 of rsqrt(2-r^2)-r^2

Lösung

\int_{0}^{1} r 2 - r^{2} - r^{2} d r

\frac{2 2 - 1}{3} - \frac{1}{3}

Dezimale

0.27614 \dots

Schritte zur Lösung

\int_{0}^{1} r 2 - r^{2} - r^{2} d r

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} r 2 - r^{2} d r - \int_{0}^{1} r^{2} d r

\int_{0}^{1} r 2 - r^{2} d r = \frac{2 2 - 1}{3}

\int_{0}^{1} r^{2} d r = \frac{1}{3}

= \frac{2 2 - 1}{3} - \frac{1}{3}