integral from 0 to 1 of x*sin(x^2)

Lösung

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

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

Dezimale

0.22984 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \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}

Berechne die Grenzen:

- cos (1) + 1

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

\int_{0}^{1} (ln (x)) d x

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