integral from pi to x of cos(2x)

Lösung

\int_{π}^{x} cos (2 x) d x

\frac{1}{2} sin (2 x)

Schritte zur Lösung

\int_{π}^{x} cos (2 x) d x

Wende U-Substitution an

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{2 π}^{2 x} cos (u) d u

Nutze das gemeinsame Integral :

\int cos (u) d u = sin (u)

= \frac{1}{2} [sin (u)]_{2 π}^{2 x}

Berechne die Grenzen:

sin (2 x)

= \frac{1}{2} sin (2 x)

\int_{0}^{\frac{π}{4}} x^{2} cos (x) d x

\int_{0}^{t} 5 d t

\int_{0}^{1} e^{- x} - e^{x} d x

\int_{0}^{1} 2 π x (x - x^{4}) d x

\int_{- 1}^{1} (y^{2} - 2 - e^{y}) d y