integral from 0 to t of sin(3t)

Lösung

\int_{0}^{t} sin (3 t) d t

\frac{1}{3} (- cos (3 t) + 1)

Schritte zur Lösung

\int_{0}^{t} sin (3 t) d t

Wende U-Substitution an

= \int_{0}^{3 t} sin (u) \frac{1}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{0}^{3 t} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{3} [- cos (u)]_{0}^{3 t}

Berechne die Grenzen:

- cos (3 t) + 1

= \frac{1}{3} (- cos (3 t) + 1)

\int_{- 2}^{1} (x^{3} + 2 x) d x

\int_{0}^{2} 3 r - r^{2} sin (θ) d r

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

\int_{1}^{2} (5 x) d x

\int_{0}^{2} sin (\frac{π x}{2}) d x