integral from pi/3 to pi/2 of (x+cos(x))

Lösung

\int_{\frac{π}{3}}^{\frac{π}{2}} (x + cos (x)) d x

\frac{5 π ^{2}}{72} + 1 - \frac{3}{2}

Dezimale

0.81936 \dots

Schritte zur Lösung

\int_{\frac{π}{3}}^{\frac{π}{2}} x + cos (x) 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_{\frac{π}{3}}^{\frac{π}{2}} x d x + \int_{\frac{π}{3}}^{\frac{π}{2}} cos (x) d x

\int_{\frac{π}{3}}^{\frac{π}{2}} x d x = \frac{5 π ^{2}}{72}

\int_{\frac{π}{3}}^{\frac{π}{2}} cos (x) d x = 1 - \frac{3}{2}

= \frac{5 π ^{2}}{72} + 1 - \frac{3}{2}