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Beliebt Rechnen >

integral from 1 to 2 of xsin(x^2)

Lösung

\int_{1}^{2} x sin (x^{2}) d x

Lösung

\frac{1}{2} (- cos (4) + cos (1))

+1

Dezimale

0.59697 \dots

Schritte zur Lösung

\int_{1}^{2} x sin (x^{2}) d x

Wende U-Substitution an

= \int_{1}^{4} \frac{sin ( 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_{1}^{4} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [- cos (u)]_{1}^{4}

Berechne die Grenzen:

- cos (4) + cos (1)

= \frac{1}{2} (- cos (4) + cos (1))

Graph

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