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

Lösung

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

6

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

= 3 [sin (x)]_{- \frac{π}{2}}^{\frac{π}{2}}

Berechne die Grenzen:

2

= 3 \cdot 2

Vereinfache

= 6

\int_{0}^{\infty} e^{- a t} d t

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

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

\int_{- 1}^{2} x^{2} - 3 x - 1 d x

\int_{0}^{1} y (y + \frac{1}{2}) d y