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_{- 1}^{3} ∣ 2 - x ∣ d x

\int_{0}^{1} x^{- 1} ln (x) d x

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

\int_{0}^{2 π} sin (\frac{x}{2}) d x

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