integral from 0 to 2 of cos(x^2)x

Lösung

\int_{0}^{2} cos (x^{2}) x d x

\frac{1}{2} sin (4)

Dezimale

- 0.37840 \dots

Schritte zur Lösung

\int_{0}^{2} cos (x^{2}) x d x

Wende U-Substitution an

= \int_{0}^{4} \frac{cos ( u )}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{4} cos (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [sin (u)]_{0}^{4}

Berechne die Grenzen:

sin (4)

= \frac{1}{2} sin (4)

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