integral from 0 to pi/2 of-xcos(x)+x

Lösung

\int_{0}^{\frac{π}{2}} - x cos (x) + x d x

- \frac{π}{2} + \frac{π ^{2}}{8} + 1

Dezimale

0.66290 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} - x cos (x) + 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_{0}^{\frac{π}{2}} x cos (x) d x + \int_{0}^{\frac{π}{2}} x d x

\int_{0}^{\frac{π}{2}} x cos (x) d x = \frac{π}{2} - 1

\int_{0}^{\frac{π}{2}} x d x = \frac{π ^{2}}{8}

= - (\frac{π}{2} - 1) + \frac{π ^{2}}{8}

Vereinfache

= - \frac{π}{2} + \frac{π ^{2}}{8} + 1

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

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

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

\int_{π}^{2 π} sin (\frac{x}{2}) d x

\int_{- \infty}^{1} cos (x) d x