integral from 0 to 1 of xsin(1-x^2)

Lösung

\int_{0}^{1} x sin (1 - x^{2}) d x

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

Dezimale

0.22984 \dots

Schritte zur Lösung

\int_{0}^{1} x sin (1 - x^{2}) d x

Wende U-Substitution an

= \int_{1}^{0} - \frac{sin ( u )}{2} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{1} - \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_{0}^{1} sin (u) d u)

Nutze das gemeinsame Integral :

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

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

Vereinfache

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

Berechne die Grenzen:

- cos (1) + 1

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

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