integral from 0 to pi of (sin(x)-cos(x))

Lösung

\int_{0}^{π} (sin (x) - cos (x)) d x

2

Schritte zur Lösung

\int_{0}^{π} sin (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_{0}^{π} sin (x) d x - \int_{0}^{π} cos (x) d x

\int_{0}^{π} sin (x) d x = 2

\int_{0}^{π} cos (x) d x = 0

= 2 - 0

Vereinfache

= 2

\int_{0}^{1} \frac{x}{1 + x} d x

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

\int_{0}^{\frac{π}{2}} x sin (n x) d x

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

\int_{\frac{π}{4}}^{\frac{π}{2}} cot^{2} (x) d x