integral from 0 to 3 of cos(pix)

Lösung

\int_{0}^{3} cos (π x) d x

0

Schritte zur Lösung

\int_{0}^{3} cos (π x) d x

Wende U-Substitution an

= \int_{0}^{π 3} cos (u) \frac{1}{π} d u

Entferne die Konstante:

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

= \frac{1}{π} \cdot \int_{0}^{π 3} cos (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{π} [sin (u)]_{0}^{π 3}

Berechne die Grenzen:

0

= \frac{1}{π} \cdot 0

Vereinfache

= 0

\int_{0}^{r} (r - \frac{r ^{3}}{r ^{2}}) d r

\int_{0}^{π} sin^{3} (x) d x

\int_{2}^{4} y^{2} d y

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

\int_{- \frac{1}{2}}^{\frac{5}{4}} x^{3} d x