integral from 1 to 3 of xsin(x^2)

Lösung

\int_{1}^{3} x sin (x^{2}) d x

\frac{1}{2} (- cos (9) + cos (1))

Dezimale

0.72571 \dots

Schritte zur Lösung

\int_{1}^{3} x sin (x^{2}) d x

Wende U-Substitution an

= \int_{1}^{9} \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}^{9} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [- cos (u)]_{1}^{9}

Berechne die Grenzen:

- cos (9) + cos (1)

= \frac{1}{2} (- cos (9) + cos (1))

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\int_{- \frac{π}{2}}^{\frac{π}{2}} sin (t) d t