integral from 0 to pi/2 of 8cos(x)sin(sin(x))

Lösung

\int_{0}^{\frac{π}{2}} 8 cos (x) sin (sin (x)) d x

8 (- cos (1) + 1)

Dezimale

3.67758 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} 8 cos (x) sin (sin (x)) d x

Entferne die Konstante:

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

= 8 \cdot \int_{0}^{\frac{π}{2}} cos (x) sin (sin (x)) d x

Wende U-Substitution an

= 8 \cdot \int_{0}^{1} sin (u) d u

Nutze das gemeinsame Integral :

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

= 8 [- cos (u)]_{0}^{1}

Berechne die Grenzen:

- cos (1) + 1

= 8 (- cos (1) + 1)

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