integral from 0 to 1 of cos(pi/2 t)

Lösung

\int_{0}^{1} cos (\frac{π}{2} t) d t

\frac{2}{π}

Dezimale

0.63661 \dots

Schritte zur Lösung

\int_{0}^{1} cos (\frac{π}{2} t) d t

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \int_{0}^{1} cos (\frac{π t}{2}) d t

Wende U-Substitution an

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

Entferne die Konstante:

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

= \frac{2}{π} \cdot \int_{0}^{\frac{π}{2}} cos (u) d u

Nutze das gemeinsame Integral :

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

= \frac{2}{π} [sin (u)]_{0}^{\frac{π}{2}}

Berechne die Grenzen:

1

= \frac{2}{π} \cdot 1

Vereinfache

= \frac{2}{π}

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