integral from 0 to 1 of cos(sqrt(x))

Lösung

\int_{0}^{1} cos (x) d x

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

Dezimale

0.76354 \dots

Schritte zur Lösung

\int_{0}^{1} cos (x) d x

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Berechne die Grenzen:

sin (1) + cos (1) - 1

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

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