integral from 0 to 1 of ycos(y^2)

Lösung

\int_{0}^{1} y cos (y^{2}) d y

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

Dezimale

0.42073 \dots

Schritte zur Lösung

\int_{0}^{1} y cos (y^{2}) d y

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

sin (1)

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

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