integral from 0 to 2 of x^2sin(x^3)

Lösung

\int_{0}^{2} x^{2} sin (x^{3}) d x

\frac{1}{3} (- cos (8) + 1)

Dezimale

0.38183 \dots

Schritte zur Lösung

\int_{0}^{2} x^{2} sin (x^{3}) d x

Wende U-Substitution an

= \int_{0}^{8} \frac{sin ( u )}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{0}^{8} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{3} [- cos (u)]_{0}^{8}

Berechne die Grenzen:

- cos (8) + 1

= \frac{1}{3} (- cos (8) + 1)

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