integral from 1 to 2 of cos(sqrt(x-1))

Lösung

\int_{1}^{2} cos (x - 1) d x

2 (sin (1) + cos (1) - 1)

Dezimale

0.76354 \dots

Schritte zur Lösung

\int_{1}^{2} cos (x - 1) d x

Wende U-Substitution an

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

Wende U-Substitution an

= \int_{0}^{1} cos (v) \cdot 2 v d v

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{1} cos (v) v d v

Wende die partielle Integration an

= 2 [v sin (v) - \int sin (v) d v]_{0}^{1}

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

= 2 [v sin (v) - (- cos (v))]_{0}^{1}

Vereinfache

= 2 [v sin (v) + cos (v)]_{0}^{1}

Berechne die Grenzen:

sin (1) + cos (1) - 1

= 2 (sin (1) + cos (1) - 1)

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