integral from 0 to x of 1/2 sin(t)

Lösung

\int_{0}^{x} \frac{1}{2} sin (t) d t

\frac{1}{2} (- cos (x) + 1)

Schritte zur Lösung

\int_{0}^{x} \frac{1}{2} sin (t) d t

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{x} sin (t) d t

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [- cos (t)]_{0}^{x}

Berechne die Grenzen:

- cos (x) + 1

= \frac{1}{2} (- cos (x) + 1)

\int_{- 2}^{2} \frac{x ^{2}}{3} - \frac{4}{3} d x

\int_{0}^{25} - 6 x d x

\int_{0}^{\infty} x^{\frac{1}{2}} d x

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

\int_{2}^{x} sin (x) e^{x} d x