integral from 0 to pi/2 of cos(kx)

Lösung

\int_{0}^{\frac{π}{2}} cos (k x) d x

\frac{sin ( \frac{πk}{2} )}{k}

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} cos (k x) d x

Wende U-Substitution an

= \int_{0}^{\frac{πk}{2}} \frac{cos ( u )}{k} d u

Entferne die Konstante:

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

= \frac{1}{k} \cdot \int_{0}^{\frac{πk}{2}} cos (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{k} [sin (u)]_{0}^{\frac{πk}{2}}

Berechne die Grenzen:

sin (\frac{πk}{2})

= \frac{1}{k} sin (\frac{πk}{2})

Vereinfache

= \frac{sin ( \frac{πk}{2} )}{k}

\int_{- 1}^{1} \frac{6}{1 + 36 t ^{2}} d t

\int_{0}^{2 π} sin (x) cos^{3} (x) d x

\int_{12}^{16} (y^{2} - 6)^{\frac{1}{2}} d y

\int_{0}^{2} k x (2 - x) d x

\int_{0}^{1} 3 x e^{2 x} d x