integral from 0 to 1 of 7cos((pix)/2)

Lösung

\int_{0}^{1} 7 cos (\frac{π x}{2}) d x

\frac{14}{π}

Dezimale

4.45633 \dots

Schritte zur Lösung

\int_{0}^{1} 7 cos (\frac{π x}{2}) d x

Entferne die Konstante:

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

= 7 \cdot \int_{0}^{1} cos (\frac{π x}{2}) d x

Wende U-Substitution an

= 7 \cdot \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

= 7 \cdot \frac{2}{π} \cdot \int_{0}^{\frac{π}{2}} cos (u) d u

Nutze das gemeinsame Integral :

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

= 7 \cdot \frac{2}{π} [sin (u)]_{0}^{\frac{π}{2}}

Vereinfache

7 \cdot \frac{2}{π} [sin (u)]_{0}^{\frac{π}{2}} : \frac{14}{π} [sin (u)]_{0}^{\frac{π}{2}}

= \frac{14}{π} [sin (u)]_{0}^{\frac{π}{2}}

Berechne die Grenzen:

1

= \frac{14}{π} \cdot 1

Vereinfache

= \frac{14}{π}

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